A154968 a(n) = 4*a(n-1) + 12*a(n-2), n>2 with a(0)=1, a(1)=1, a(2)=7.

1, 1, 7, 40, 244, 1456, 8752, 52480, 314944, 1889536, 11337472, 68024320, 408146944, 2448879616, 14693281792, 88159682560, 528958111744, 3173748637696, 19042491891712, 114254951219200, 685529707577344

Offset: 0

Author

Philippe Deléham, Jan 18 2009

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,12).

Crossrefs

Cf. A154929.

Programs

Magma

[n eq 0 select 1 else (6^(n+1) -(-2)^(n+1))/32: n in [0..40]]; // G. C. Greubel, Mar 01 2021

Mathematica

LinearRecurrence[{4,12}, {1,1,7}, 40] (* G. C. Greubel, Mar 01 2021 *)

SageMath

[1]+[(6^(n+1) - (-2)^(n+1))/32 for n in [1..40]] # G. C. Greubel, Mar 01 2021

Formula

16*a(n) = 3*6^n +(-1)^n*2^n, n>0. - R. J. Mathar, Sep 03 2013

From G. C. Greubel, Mar 01 2021: (Start)

a(n) = (6^(n+1) - (-2)^(n+1))/32 + (3/4)*[n=0].

E.g.f.: (exp(-2*x) + 3*exp(6*x))/16. (End)