A111766 - OEIS

This site is supported by donations to The OEIS Foundation.

A111766

Numbers occurring in three Pythagorean triples of the form: odd: a, (a^2-1)/2, (a^2+1)/2 OR even: a, a^2/4-1, a^2/4+1.

0, 5, 24, 145, 840, 4901, 28560, 166465, 970224, 5654885, 32959080, 192099601, 1119638520, 6525731525, 38034750624, 221682772225, 1292061882720, 7530688524101, 43892069261880, 255821727047185 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,2`
	COMMENTS	`This parallels Cassini's identity for Fibonacci numbers (Mathworld)`
	LINKS	`Index to sequences with linear recurrences with constant coefficients, signature (5,5,-1).`
	FORMULA	`a(n) = A000129(n-1)A000129(n+1) = A000129(n)^2 + (-1)^n.` `G.f. -x(-5+x) / ( (1+x)(1-6x+x^2) ). - R. J. Mathar, Sep 21 2011`
	EXAMPLE	`e.g. a(5) = P(4)P(6) = 1270 = 840 = P(5)-1 = 29^2-1`
	CROSSREFS	`Cf. A076218, A078522 (bisections).` `Sequence in context: A080996 A020055 A201952 * A009424 A184597 A009601` `Adjacent sequences: A111763 A111764 A111765 * A111767 A111768 A111769`
	KEYWORD	`nonn`
	AUTHOR	`Jeremy C. Buchanan (jbuchanan(AT)myhww.org), Nov 21 2005`

Content is available under The OEIS End-User License Agreement .

Last modified February 17 10:05 EST 2012. Contains 206009 sequences.