A158064 a(n) = 36*n^2 + 2*n.

38, 148, 330, 584, 910, 1308, 1778, 2320, 2934, 3620, 4378, 5208, 6110, 7084, 8130, 9248, 10438, 11700, 13034, 14440, 15918, 17468, 19090, 20784, 22550, 24388, 26298, 28280, 30334, 32460, 34658, 36928, 39270, 41684, 44170, 46728, 49358, 52060

Offset: 1

Author

Vincenzo Librandi, Mar 12 2009

Keywords

• nonn
• easy

Comments

The identity (36*n + 1)^2 - (36*n^2 + 2*n)*6^2 = 1 can be written as A158065(n)^2 - a(n)*6^2 = 1. - Vincenzo Librandi, Feb 11 2012

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(6^2*t+2)).
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A158065.

Programs

Magma

I:=[38, 148, 330]; [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 11 2012

Mathematica

LinearRecurrence[{3, -3, 1}, {38, 148, 330}, 50] (* Vincenzo Librandi, Feb 11 2012 *)

PARI

for(n=1, 40, print1(36*n^2 + 2*n", ")); \\ Vincenzo Librandi, Feb 11 2012

Formula

G.f.: 2*x*(-19 - 17*x)/(x-1)^3. - Vincenzo Librandi, Feb 11 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 11 2012