A157324 a(n) = 36*n^2 + n.

37, 146, 327, 580, 905, 1302, 1771, 2312, 2925, 3610, 4367, 5196, 6097, 7070, 8115, 9232, 10421, 11682, 13015, 14420, 15897, 17446, 19067, 20760, 22525, 24362, 26271, 28252, 30305, 32430, 34627, 36896, 39237, 41650, 44135, 46692, 49321, 52022

Offset

1,1

Comments

The identity (10368*n^2 + 288*n + 1)^2 - (36*n^2 + n)*(1728*n + 24)^2 = 1 can be written as A157326(n)^2 - a(n)*A157325(n)^2 = 1.

This is the case s=6 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 26 2012

Links

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

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

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

Formula

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 26 2012

G.f.: x*(-37 - 35*x)/(x-1)^3. - Vincenzo Librandi, Jan 26 2012

Mathematica

LinearRecurrence[{3, -3, 1}, {37, 146, 327}, 50] (* Vincenzo Librandi, Jan 26 2012 *)
Table[36n^2+n, {n, 50}] (* Harvey P. Dale, Mar 09 2019 *)

Prog

(Magma) I:=[37, 146, 327]; [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 26 2012
(PARI) for(n=1, 40, print1(36*n^2 + n", ")); \\ Vincenzo Librandi, Jan 26 2012

Crossrefs

Cf. A157325, A157326.

Sequence in context: A262318 A262921 A031690 * A251113 A251106 A141968

Adjacent sequences: A157321 A157322 A157323 * A157325 A157326 A157327

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 27 2009

Status

approved