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Topic: Motzkin number

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	tingilinde: take a number ...
		22 is the number of partitions of 8.
		101 is the number of partitions of 13.
		231 is the number of partitions of 16.
	tingilinde.typepad.com /starstuff/2005/11/significant_int.html (12385 words)

	Интересные числа на Арбузе (1)
		is the number of planar partitions of 10.
		is the number of planar partitions of 11.
		is the number of planar partitions of 12.
	arbuz.uz /z_numbers1.html (3969 words)

	Интересные числа 2
		is the number of planar partitions of 17.
		is the number of planar partitions of 18.
		is the number of planar partitions of 19.
	arbuz.uz /z_numbers2.html (3655 words)

	9 (number) - Wikipedia, the free encyclopedia
		Nine is a composite number, its proper divisors being 1 and 3.
		Nine is the number of Valkyries in Richard Wagner's Die Walküre.
		Nine is the number of musicians in a nonet.
	en.wikipedia.org /wiki/9_(number) (2429 words)

	Motzkin number - Wikipedia, the free encyclopedia
		A Motzkin number for a given number n is the number of different ways of drawing non-intersecting chords on a circle between n points.
		The Motzkin number for n is also the number of positive integer sequences n−1 long in which the opening and ending elements are either 1 or 2, and the difference between any two consecutive elements is −1, 0 or 1.
		All together, there are at least fourteen different manifestations of Motzkin numbers in different branches of mathematics, as enumerated by Donaghey and Shapiro in their 1977 survey of Motzkin numbers.
	en.wikipedia.org /wiki/Motzkin_number (234 words)

	Motzkin biography
		Motzkin already had several publications before his thesis on linear programming was completed in 1934.
		In 1935 Motzkin was appointed to the Hebrew University in Jerusalem.
		The proof is very typical of Motzkin in that the Euclidean algorithm is given a new formulation, which at first seems to be leading away from the problem at hand, but is suddenly seen to be the decisive key to its solution.
	www-gap.dcs.st-and.ac.uk /~history/Biographies/Motzkin.html (1174 words)

	What's Special About This Number?
		is the number of planar partitions of 9.
		is the smallest number with the property that it and its neighbors are not cubefree.
		is a number whose sum of squares of the divisors is a square.
	www.stetson.edu /~efriedma/numbers.html (7473 words)

	Million - Wikipedia, the free encyclopedia
		Artistic depiction of the well-known, large, round number emblazoned in gold.
		The word "million" is common to the short scale and long scale numbering systems (and also to the proposed Rowlett numbering system), unlike the larger numbers, which have different names in the two systems.
		This word is the most common of words ending in -lion, and the fact that in English it does not have a distinct pronunciation due to its double 'll' causes endless spelling confusion with 'vermilion', 'pavilion', etc.
	en.wikipedia.org /wiki/Million (482 words)

	Bruce Litow, Philippe Dumas. Additive Cellular Automata and Algebraic Series.
		We see the evolution of the automaton for the cells, which have a number between -11 and 2, in the figure 1.
		6] is defined by the following procedure: one folds a sheet of paper an infinite number of times always in the same direction; next one unfolds it and one codes the sequence of the folds by 0 or 1 according to their up or down position.
		The number l is the length of the path.
	pauillac.inria.fr /algo/dumas/LiDu93/Html/index.html (1427 words)

	1000000 (number) - Biocrawler (Site not responding. Last check: 2007-10-31)
		The million is sometimes used in the English language as a metaphor for a very large number, as in "Never in a million years" and "You're one in a million", or a hyperbole, as in "I've walked a million miles".
		Orders of magnitude (numbers) to help compare dimensionless numbers between 1 000 000 and 10 000 000 (10
		1048576 = 2^20 (power of two); 2116-gonal number, an 8740-gonal number and a 174764-gonal number; the number of bytes in a mebibyte, the number of kibibytes in a gibibyte, and so on.
	www.biocrawler.com /encyclopedia/1_E6 (314 words)

	Notes by David Callan (Site not responding. Last check: 2007-10-31)
		We show that Kreweras's identity counts Dyck paths with a given number of peaks by number of peak plateaus, where a peak plateau is a run of consecutive peaks that is preceded by an upstep and followed by a downstep.
		Regarding Pascal's matrix and a recursion for Bernoulli numbers.
		Also, we give a "walk around"-type bijection between the "bushes" and "paths" that are counted by Motzkin numbers and show how it applies to those counted by Schröder numbers.
	www.stat.wisc.edu /~callan/papersother (498 words)

	9th - The real meaning from Timesharetalk wikipedia
		Another consequence of 9 being 10 - 1, is that it is also a Kaprekar number.
		pinyin jiu) is considered a good number in Chinese culture because it sounds the same as the word "longlasting" (?
		Perhaps Antonín Dvorák was also superstitious about the number nine, because he wrote no symphonies after his New World Symphony, which is nowadays considered his Ninth, but which he thought of was his Eighth because he considered the score of his early C minor symphony lost forever.
	www.timesharetalk.co.uk /wiki.asp?k=9th (2431 words)

	Catwalks, Sandsteps and Pascal Pyramids
		Their number is the same as the total number of paths already counted, except that y is replaced by y+2, i.e., r and s are each decreased by 1.
		For a given path, say C, of such a random walk the total number of paths is found which, after each step, do not lie to the left of the corresponding point of C, and which touch C in a prescribed way in exactly r of the last s left steps.
		The number of ``good paths'' from p to q is the total number of paths from p to q minus the number of ``bad paths'' from p to q (those which touch the line).
	www.cs.uwaterloo.ca /journals/JIS/VOL3/GUY/catwalks.html (7889 words)

	The On-Line Encyclopedia of Integer Sequences
		Difference array of Motzkin numbers A001006 read by antidiagonals.
		Row sums of even rows equal the Motzkin number of the next row - n!/((n/2)!((n/2)+1)!) (i.e.
		F. Bernhart, Catalan, Motzkin and Riordan numbers, Discr.
	www.research.att.com /~njas/sequences/A059347 (119 words)

	The Number 9 (Site not responding. Last check: 2007-10-31)
		The Chemical Element Beryllium has an atomic number of 9.
		The Chemical Element Fluorine has one Stable Isotope.
		The nine was the key number of teaching for the materialistic Hindu philosophers in the Vaiceshika school.
	www.virtuescience.com /9.html (343 words)

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