id:A158632 - OEIS Search Results

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a(n)=46*n^2+1.

+0
2

1, 47, 185, 415, 737, 1151, 1657, 2255, 2945, 3727, 4601, 5567, 6625, 7775, 9017, 10351, 11777, 13295, 14905, 16607, 18401, 20287, 22265, 24335, 26497, 28751, 31097, 33535, 36065, 38687, 41401, 44207, 47105, 50095, 53177, 56351, 59617, 62975 (list; graph; listen)

	OFFSET	`0,2`
	COMMENT	`The identity (46n^2+1)^2 - (529n^2+23) * (2n)^2 = 1 can be written as` `the Pell equation (a(n))^2 - A158631(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+44x+47x^2)/(x-1)^3.`
	CROSSREFS	`Cf. A005843, A158631` `Sequence in context: A078857 A139992 A142916 this_sequence A142413 A065532 A157362` `Adjacent sequences: A158629 A158630 A158631 this_sequence A158633 A158634 A158635`
	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 2 11:54 EST 2009. Contains 167921 sequences.

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