id:A158537 - OEIS Search Results

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22*n^2+1.

+0
2

1, 23, 89, 199, 353, 551, 793, 1079, 1409, 1783, 2201, 2663, 3169, 3719, 4313, 4951, 5633, 6359, 7129, 7943, 8801, 9703, 10649, 11639, 12673, 13751, 14873, 16039, 17249, 18503, 19801, 21143, 22529, 23959, 25433, 26951, 28513, 30119, 31769 (list; graph; listen)

	OFFSET	`0,2`
	COMMENT	`From the Pell-type identity (22n^2+1)^2 - (121n^2+11) * (2n)^2 = 1 we derive` `(a(n))^2 - A158536(n) (A005843(n))^2 = 1.`
	LINKS	`Vincenzo Librandi, X^2-AY^2=1` `Wolfram MathWorld, Pell Equation` `Edward Everett Withford, Pell Equation`
	FORMULA	`a(n)= 3a(n-1) -3a(n-2) +a(n-3). G.f.: (1+20x+23x^2)/(1-x)^3.`
	CROSSREFS	`Cf. A005843, A158536` `Sequence in context: A044591 A050255 A014088 this_sequence A117049 A142062 A050529` `Adjacent sequences: A158534 A158535 A158536 this_sequence A158538 A158539 A158540`
	KEYWORD	`nonn,easy`
	AUTHOR	`Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 21 2009`
	EXTENSIONS	`Comment rewritten, a(0) added - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 16 2009`

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Last modified December 10 12:37 EST 2009. Contains 170569 sequences.

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