id:A158644 - OEIS Search Results

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a(n)=52*n^2+1.

+0
2

1, 53, 209, 469, 833, 1301, 1873, 2549, 3329, 4213, 5201, 6293, 7489, 8789, 10193, 11701, 13313, 15029, 16849, 18773, 20801, 22933, 25169, 27509, 29953, 32501, 35153, 37909, 40769, 43733, 46801, 49973, 53249, 56629, 60113, 63701, 67393 (list; graph; listen)

	OFFSET	`0,2`
	COMMENT	`The identity (52n^2+1)^2 - (676n^2+26) * (2n)^2 = 1 can be written as` `the Pell equation (a(n))^2 - A158643(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+50x+53x^2)/(x-1)^3.`
	CROSSREFS	`Cf. A005843, A158643` `Sequence in context: A008993 A142088 A005146 this_sequence A158656 A142000 A053652` `Adjacent sequences: A158641 A158642 A158643 this_sequence A158645 A158646 A158647`
	KEYWORD	`nonn,easy`
	AUTHOR	`Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 23 2009`
	EXTENSIONS	`Comment rephrased and redundant formula replaced by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 19 2009`

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Last modified December 19 12:50 EST 2009. Contains 171053 sequences.

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