A078522 - OEIS

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A078522

Numbers n such that (n+1)(2n+1) is a perfect square. Equivalently, both n+1 and 2n+1 are perfect squares.

0, 24, 840, 28560, 970224, 32959080, 1119638520, 38034750624, 1292061882720, 43892069261880, 1491038293021224, 50651409893459760, 1720656898084610640, 58451683124983302024, 1985636569351347658200, 67453191674820837076800 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,2`
	LINKS	`Index to sequences with linear recurrences with constant coefficients, signature (35,-35,1).`
	FORMULA	`a(1)=0; a(2)=24; a(n)=34a(n-1)-a(n-2)+24; a(n)=floor(AB^n) where A=(3+2sqrt(2))/8 and B=17+12sqrt(2); a(n)=A008844(n)-1. - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 19 2003` `G.f. -24x^2 / ( (x-1)(x^2-34x+1) ). a(n) = 24A029546(n-2). - R. J. Mathar, Sep 21 2011`
	MATHEMATICA	`a[0]=0; a[1]=24; a[n_] := a[n]=34a[n-1]-a[n-2]+24`
	CROSSREFS	`The square roots of (n+1)(2n+1) are in A046176.` `Sequence in context: A175604 A158651 A204559 * A195130 A005149 A027411` `Adjacent sequences: A078519 A078520 A078521 * A078523 A078524 A078525`
	KEYWORD	`nonn`
	AUTHOR	`Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Jan 07 2003`

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Last modified February 16 04:47 EST 2012. Contains 205860 sequences.