id:A158591 - OEIS Search Results

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a(n)=36*n^2+1.

+0
2

1, 37, 145, 325, 577, 901, 1297, 1765, 2305, 2917, 3601, 4357, 5185, 6085, 7057, 8101, 9217, 10405, 11665, 12997, 14401, 15877, 17425, 19045, 20737, 22501, 24337, 26245, 28225, 30277, 32401, 34597, 36865, 39205, 41617, 44101, 46657, 49285, 51985 (list; graph; listen)

	OFFSET	`0,2`
	COMMENT	`The identity (36n^2+1)^2 - (324n^2+18)(2n)^2 = 1 can be written in` `Pell-format as (a(n))^2 - A158590(n)* (A005843(n))^2 =1.`
	LINKS	`Vincenzo Librandi, X^2-AY^2=1` `Edward Everett Withford, Pell Equation` `Wolfram MathWorld, Pell Equation`
	FORMULA	`a(n)= 3a(n-1) -3a(n-2) +a(n-3). G.f: -(1+34x+37x^2)/(x-1)^3.`
	CROSSREFS	`Cf. A005843, A158590` `Sequence in context: A044750 A141936 A142498 this_sequence A031690 A157324 A141968` `Adjacent sequences: A158588 A158589 A158590 this_sequence A158592 A158593 A158594`
	KEYWORD	`nonn,easy`
	AUTHOR	`Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 22 2009`
	EXTENSIONS	`Comment rewritten, formula replaced by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 28 2009`

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Last modified November 30 13:13 EST 2009. Contains 167758 sequences.

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