A154517 a(n) = 9*n^2 + n.

10, 38, 84, 148, 230, 330, 448, 584, 738, 910, 1100, 1308, 1534, 1778, 2040, 2320, 2618, 2934, 3268, 3620, 3990, 4378, 4784, 5208, 5650, 6110, 6588, 7084, 7598, 8130, 8680, 9248, 9834, 10438, 11060, 11700, 12358, 13034, 13728, 14440

Offset: 1

Author

Vincenzo Librandi, Jan 11 2009

Keywords

• nonn
• easy

Comments

The identity (648*n^2 + 72*n + 1)^2 - (9*n^2 + n)*(216*n + 12)^2 = 1 can be written as A154515(n)^2 - a(n)*A154519(n)^2 = 1 (see also the second comment at A154515). - Vincenzo Librandi, Jan 31 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).

Crossrefs

Cf. A154515, A154519.

Programs

Magma

I:=[10, 38, 84]; [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 31 2012

Mathematica

LinearRecurrence[{3, -3, 1}, {10, 38, 84}, 50] (* Vincenzo Librandi, Jan 31 2012 *)

PARI

a(n)=9*n^2+n \\ Charles R Greathouse IV, Dec 27 2011

Formula

G.f.: x*(-10 - 8*x)/(x-1)^3. - Vincenzo Librandi, Jan 31 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 31 2012