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A158550 a(n) = 169*n^2 - 13. 2
156, 663, 1508, 2691, 4212, 6071, 8268, 10803, 13676, 16887, 20436, 24323, 28548, 33111, 38012, 43251, 48828, 54743, 60996, 67587, 74516, 81783, 89388, 97331, 105612, 114231, 123188, 132483, 142116, 152087, 162396, 173043, 184028, 195351 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (26*n^2 - 1)^2 - (169*n^2 - 13)*(2*n)^2 = 1 can be written as A158551(n)^2 - a(n)*A005843(n)^2 = 1.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

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

FORMULA

G.f.: 13*x*(-12 - 15*x + x^2)/(x-1)^3.

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

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {156, 663, 1508}, 40] (* Vincenzo Librandi, Feb 14 2012 *)

169*Range[40]^2-13 (* Harvey P. Dale, Apr 12 2017 *)

PROG

(MAGMA) I:=[156, 663, 1508]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 14 2012

(PARI) for(n=1, 40, print1(169*n^2 - 13", ")); \\ Vincenzo Librandi, Feb 14 2012

CROSSREFS

Cf. A005843, A158551.

Sequence in context: A259947 A043356 A038476 * A156994 A304619 A204718

Adjacent sequences:  A158547 A158548 A158549 * A158551 A158552 A158553

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 21 2009

EXTENSIONS

Comment rewritten by R. J. Mathar, Oct 16 2009

STATUS

approved

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Last modified August 17 12:02 EDT 2022. Contains 356189 sequences. (Running on oeis4.)