id:A158693 - OEIS Search Results

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a(n)=66*n^2-1.

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65, 263, 593, 1055, 1649, 2375, 3233, 4223, 5345, 6599, 7985, 9503, 11153, 12935, 14849, 16895, 19073, 21383, 23825, 26399, 29105, 31943, 34913, 38015, 41249, 44615, 48113, 51743, 55505, 59399, 63425, 67583, 71873, 76295, 80849, 85535 (list; graph; listen)

	OFFSET	`1,1`
	COMMENT	`The identity (66n^2-1)^2 - (1089n^2-33) * (2n)^2 = 1 can be written as` `the Pell equation (a(n))^2 - A158692(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(-65-68x+x^2)/(x-1)^3.`
	CROSSREFS	`Cf. A005843, A158692` `Sequence in context: A031694 A152023 A165798 this_sequence A069758 A116678 A020292` `Adjacent sequences: A158690 A158691 A158692 this_sequence A158694 A158695 A158696`
	KEYWORD	`nonn,easy`
	AUTHOR	`Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 24 2009`
	EXTENSIONS	`Comment rewritten and formula replaced by R. J. Mathar, (mathar(AT)strw.leidenuniv.nl), Oct 22 2009`

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Last modified December 4 08:07 EST 2009. Contains 170310 sequences.

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