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A158586 a(n) = 34*n^2 + 1. 2
1, 35, 137, 307, 545, 851, 1225, 1667, 2177, 2755, 3401, 4115, 4897, 5747, 6665, 7651, 8705, 9827, 11017, 12275, 13601, 14995, 16457, 17987, 19585, 21251, 22985, 24787, 26657, 28595, 30601, 32675, 34817, 37027, 39305, 41651, 44065, 46547, 49097 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The identity (34*n^2 + 1)^2 - (289*n^2 + 17)*(2*n)^2 = 1 can be written as a(n)^2 - A158585(n)*A005843(n)^2 = 1.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Vincenzo Librandi, X^2-AY^2=1

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

G.f.: (1 + 32*x + 35*x^2)/(1-x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {1, 35, 137}, 50] (* Vincenzo Librandi, Feb 15 2012 *)

PROG

(Magma) I:=[1, 35, 137]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 15 2012

(PARI) for(n=0, 50, print1(34*n^2 + 1", ")); \\ Vincenzo Librandi, Feb 15 2012

CROSSREFS

Cf. A005843, A158585.

Sequence in context: A044367 A044748 A171473 * A350205 A267565 A330230

Adjacent sequences:  A158583 A158584 A158585 * A158587 A158588 A158589

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 22 2009

EXTENSIONS

Comment rewritten, a(0) added by R. J. Mathar, Oct 16 2009

STATUS

approved

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Last modified September 28 07:19 EDT 2022. Contains 357063 sequences. (Running on oeis4.)