A158604 - OEIS

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A158604

a(n)=42*n^2+1.

1, 43, 169, 379, 673, 1051, 1513, 2059, 2689, 3403, 4201, 5083, 6049, 7099, 8233, 9451, 10753, 12139, 13609, 15163, 16801, 18523, 20329, 22219, 24193, 26251, 28393, 30619, 32929, 35323, 37801, 40363, 43009, 45739, 48553, 51451, 54433, 57499 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,2`
	COMMENTS	`The identity (42n^2+1)^2 - (441n^2+21)(2n)^2 = 1 can be written in` `Pell-format as (a(n))^2 - A158603(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+40x+43x^2)/(x-1)^3.`
	CROSSREFS	`Cf. A005843, A158603` `Sequence in context: A142016 A140640 A083357 * A057816 A162295 A187722` `Adjacent sequences: A158601 A158602 A158603 * A158605 A158606 A158607`
	KEYWORD	`nonn,easy`
	AUTHOR	`Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 22 2009`
	EXTENSIONS	`Comment rewritten, formula replaced by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 28 2009`

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Last modified February 16 01:56 EST 2012. Contains 205860 sequences.