A154514 a(n) = 648*n^2 - 72*n + 1.

577, 2449, 5617, 10081, 15841, 22897, 31249, 40897, 51841, 64081, 77617, 92449, 108577, 126001, 144721, 164737, 186049, 208657, 232561, 257761, 284257, 312049, 341137, 371521, 403201, 436177, 470449, 506017, 542881, 581041, 620497, 661249

Offset

1,1

Comments

The identity (648*n^2 - 72*n + 1)^2 - (9*n^2 - n)*(216*n - 12)^2 = 1 can be written as a(n)^2 - A154516(n)*A154518(n)^2 = 1. This is the case s=3 of the identity (8*n^2*s^4 - 8*n*s^2 + 1)^2 - (n^2*s^2 - n)*(8*n*s^3 - 4*s)^2 = 1. - Vincenzo Librandi, Jan 30 2012

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.: x*(-577 - 718*x - x^2)/(x-1)^3. - Harvey P. Dale, Apr 22 2011

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 30 2012

Mathematica

Table[648n^2-72n+1, {n, 50}] (* Harvey P. Dale, Apr 22 2011 *)

Prog

(PARI) a(n)=648*n^2-72*n+1 \\ Charles R Greathouse IV, Dec 27 2011
(Magma) I:=[577, 2449, 5617]; [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, Jan 30 2012

Crossrefs

Cf. A154516, A154518.

Sequence in context: A244095 A261889 A031726 * A278740 A101249 A202011

Adjacent sequences: A154511 A154512 A154513 * A154515 A154516 A154517

Keyword

nonn,easy

Author

Vincenzo Librandi, Jan 11 2009

Status

approved