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Topic: Square triangular number

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	Square number - Wikipedia, the free encyclopedia
		In mathematics, a square number, sometimes also called a perfect square, is an integer that can be written as the square of some other integer.
		A square number is also the sum of two consecutive triangular numbers.
		The sum of two consecutive square numbers is a centered square number.
	en.wikipedia.org /wiki/Square_number (758 words)

	What's Special About This Number?
		is the number of planar partitions of 10.
		is the number of planar partitions of 11.
		is the number of planar partitions of 12.
	www.stetson.edu /~efriedma/numbers.html (7482 words)

	Math Forum: Ask Dr. Math FAQ: Glossary of Numbers
		A happy number is a number for which the sum of the squares of the digits eventually equals 1.
		A polygonal number is the number of equally spaced dots needed to draw a polygon.
		A triangular number is the number of dots needed to draw a triangle.
	mathforum.org /dr.math/faq/faq.number.glossary.html (1533 words)

	Square triangular number - Wikipedia, the free encyclopedia
		A square triangular number (or triangular square number) is a number which is both a triangular number and a perfect square.
		There is an infinity of triangular squares, given by the formula
		Triangular numbers that are also square at cut-the-knot
	en.wikipedia.org /wiki/Triangular_square_number (161 words)

	Fascinating Triangular Numbers By Shyam Sunder Gupta
		Numbers such that d(n), the number of divisors of n, is greater than for any smaller n are called highly composite numbers.
		Number of divisors of all triangular numbers less than 28 is less than 6.
		Numbers such that s(n), the sum of aliquot divisors of n, is greater than n are called Abundant numbers.
	www.shyamsundergupta.com /triangle.htm (1716 words)

	Composite numbers and squares from recursive series
		Although square triangular numbers are well known, I haven't found a prior publication of this relationship.
		Your formula for getting the next square triangular number c^2 from a square triangular number b^2 follows from the usual way of generating the solutions to this equation, i.e.
		is always a triangular number since the constant is -1 as is the case with square triangular numbers.
	www.physicsforums.com /showthread.php?p=933057 (2158 words)

	id:A001110 - OEIS Search Results
		Numbers that are both triangular and square: a(n) = 34a(n-1) - a(n-2) + 2.
		A. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p.
		a(2) = ((17+12sqrt(2))^2+(17-12sqrt(2))^2-2)/32 = (289+24sqrt(2)+288+289-24sqrt(2)+288-2)/32 = (578+576-2)/32 = 1152/32 = 36 and 6^2 = 36 = 89/2 = >a(2) is both the sixth square* and the 8th triangular number
	www.research.att.com /projects/OEIS?Anum=A001110 (430 words)

	Triangular number that are also square
		I couldn't help dropping this note to point out the curious fact that there is also an infinite set of numbers which are simultaneously both triangular and square.
		However, (1) does not enumerate all such numbers.
		Armando Guarnaschelli from Argentina found a very simple recurrence relation that generates all triangular numbers that are also square.
	www.cut-the-knot.org /do_you_know/triSquare.shtml (312 words)

	Square Triangular Numbers (Site not responding. Last check: 2007-10-22)
		The triangular numbers are 1, 3, 6, 10, 15, 21, 28, 36, 45,...
		A standard problem in elementary number theory is to determine ALL the numbers that are both square and triangular.
		So, we've shown that n[k] is a square for every odd index k=2j-1, and of course the quantity 4n is a square if and only if n is a square, so we have the related result that the number 4 n[2j-1] = (3+2sqrt(2))^(2j-1) + (3-2sqrt(2))^(2j-1) - 2 is a square for every positive integer j.
	www.mathpages.com /home/kmath159.htm (301 words)

	More about Palindromic Squares
		Palindromic numbers are numbers which read the same from
		Square numbers are defined and calculated by this extraordinary intricate and excruciatingly complex formula.
		Unlike Palindromic Triangulars where it is impossible to predict a next higher one, whether its basenumber is palindromic or not, with the Palindromic Squares (and Cubes) we have an opposite situation.
	www.worldofnumbers.com /square.htm (2239 words)

	Table of Figurate Numbers, Sorted, Through 10,000
		For every n > 1 consider all square tilings of an n x n square, and define: f(n) = the largest possible size of the smallest square g(n) = the smallest number of squares h(n) = the smalles value of the largest multiplicity of any square needed.
		Hendecagonal Number, or 11-gonal number, Hen(16), hence the Heterogeneous Jonathan Number Hen(S(4))
		Hendecagonal Number, or 11-gonal number, Hen(25), hence the Heterogeneous Jonathan Number Hen(S(5))
	www.magicdragon.com /fig.html (10985 words)

	Amazing Number Facts No (Site not responding. Last check: 2007-10-22)
		We all know and love the Triangular Numbers
		A little calculation might produce the next example.
		If you have answers, discoveries, new questions etc to do with this Number Fact then...
	www.madras.fife.sch.uk /maths/amazingnofacts/fact017.html (83 words)

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