A290124 a(n) = a(n-1) + 12*a(n-2) with a(1) = 1 and a(2) = 2.

1, 2, 14, 38, 206, 662, 3134, 11078, 48686, 181622, 765854, 2945318, 12135566, 47479382, 193106174, 762858758, 3080132846, 12234437942, 49196032094, 196009287398, 786361672526, 3138473121302, 12574813191614, 50236490647238, 201134248946606, 803972136713462, 3217583124072734

Offset: 1

Author

Matt C. Anderson, Jul 20 2017

Keywords

• nonn
• easy

Comments

The binomial transform is 1, 3, 19, 87,.... (A015528 shifted). - R. J. Mathar, Apr 07 2022

Links

• Index entries for linear recurrences with constant coefficients, signature (1,12).

Crossrefs

Cf. A000045, A000079, A133577.

Programs

Magma

[(5/28)*4^n-(2/21)*(-3)^n: n in [1..30]]; // Vincenzo Librandi, Aug 27 2017

Mathematica

CoefficientList[Series[(1 + x) / ((1 + 3 x) (1 - 4 x)), {x, 0, 33}], x] (* Vincenzo Librandi, Aug 27 2017 *)

PARI

a(n) = if (n==1, 1, if (n==2, 2, a(n-1) + 12*a(n-2))); \\ Michel Marcus, Jul 25 2017

Formula

a(n) = (5/28)*4^n - (2/21)*(-3)^n.

G.f.: x*(1+x)/((1+3*x)*(1-4*x)). - Vincenzo Librandi, Aug 27 2017