id:A158588 - OEIS Search Results

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a(n)=34*n^2-1.

+0
2

33, 135, 305, 543, 849, 1223, 1665, 2175, 2753, 3399, 4113, 4895, 5745, 6663, 7649, 8703, 9825, 11015, 12273, 13599, 14993, 16455, 17985, 19583, 21249, 22983, 24785, 26655, 28593, 30599, 32673, 34815, 37025, 39303, 41649, 44063, 46545, 49095 (list; graph; listen)

	OFFSET	`1,1`
	COMMENT	`The identity (34n^2-1)^2 - (289n^2-17) * (2n)^2 = 1 can be written` `in Pell-type form as (a(n))^2 - A158587(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.: x(-33-36x+x^2)/(x-1)^3.`
	CROSSREFS	`Cf. A005843, A158587` `Sequence in context: A044365 A044746 A105091 this_sequence A084028 A007260 A005904` `Adjacent sequences: A158585 A158586 A158587 this_sequence A158589 A158590 A158591`
	KEYWORD	`nonn,easy`
	AUTHOR	`Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 22 2009`
	EXTENSIONS	`Comment rewritten - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 16 2009`

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.

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