A137223 a(n) = A135574(3*n) + A135574(3*n+1) + A135574(3*n+2).

3, 18, 234, 1110, 15018, 70998, 961194, 4543830, 61516458, 290805078, 3937053354, 18611524950, 251971414698, 1191137596758, 16126170540714, 76232806192470, 1032074914605738, 4878899596318038, 66052794534767274, 312249574164354390

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (-1,64,64).

Formula

From R. J. Mathar, Feb 07 2009: (Start)

a(n) = -a(n-1) + 64*a(n-2) + 64*a(n-3).

a(n) = (-8*(-1)^n + 35*8^n + 9*(-8)^n)/12.

G.f.: 3*(1 +7*x +20*x^2)/((1-8*x)*(1+8*x)*(1+x)). (End)

Mathematica

LinearRecurrence[{-1, 64, 64}, {3, 18, 234}, 41] (* G. C. Greubel, Jan 05 2022 *)

Prog

(Magma) I:=[3, 18, 234]; [n le 3 select I[n] else -Self(n-1) +64*Self(n-2) +64*Self(n-3): n in [1..30]]; // G. C. Greubel, Jan 05 2022
(Sage) [((35 + 9*(-1)^n)*8^n - 8*(-1)^n)/12 for n in (0..40)] # G. C. Greubel, Jan 05 2022

Crossrefs

Cf. A135574.

Sequence in context: A195767 A195763 A265460 * A159640 A038061 A232916

Adjacent sequences: A137220 A137221 A137222 * A137224 A137225 A137226

Keyword

nonn

Author

Paul Curtz, Mar 07 2008

Extensions

More terms from R. J. Mathar, Feb 07 2009

Status

approved