A087452 G.f.: (2-x)/((1+3x)(1-4x)); e.g.f.: exp(4x) + exp(-3x); a(n) = 4^n + (-3)^n.

2, 1, 25, 37, 337, 781, 4825, 14197, 72097, 242461, 1107625, 4017157, 17308657, 65514541, 273218425, 1059392917, 4338014017, 17050729021, 69106897225, 273715645477, 1102998412177, 4387586157901, 17623567104025, 70274600998837, 281757406247137

Offset: 0

Author

Paul Barry, Sep 06 2003

Keywords

• easy
• nonn

Comments

Generalized Lucas-Jacobsthal numbers.

Links

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

Crossrefs

Cf. A014551, A053404, A087451.

Programs

Mathematica

CoefficientList[Series[(2 - z)/((1 + 3 z) (1 - 4 z)), {z, 0, 200}], z] (* Vladimir Joseph Stephan Orlovsky, Jun 11 2011 *)
LinearRecurrence[{1,12},{2,1},30] (* Harvey P. Dale, Nov 06 2022 *)

PARI

polsym(x^2-x-12,50) \\ Charles R Greathouse IV, Jun 11 2011

Formula

a(n) = (-3)^n+4^n.

a(n) = a(n-1) + 12*a(n-2) for n > 1; a(0)=2, a(1)=1. - Philippe Deléham, Sep 19 2009

a(n) = 2*A053404(n) - A053404(n-1), n > 0. - Ralf Stephan, Jul 21 2013