A249995 Expansion of 1/((1+2*x)*(1-3*x)*(1-4*x)).

1, 5, 27, 121, 539, 2289, 9619, 39737, 162987, 663553, 2690051, 10865673, 43783195, 176086097, 707220723, 2837479129, 11375770763, 45580514721, 182554616035, 730915611305, 2925754935291, 11709295114225, 46856010770387, 187480525633401, 750091566966379, 3000874627609409

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,2,-24).

Formula

G.f.: 1/((1+2*x)*(1-3*x)*(1-4*x)).

a(n) = ((-1)^n*2^(n+1) + 5*2^(2*n+3) - 3^(n+3))/15. - Colin Barker, Dec 29 2014

a(n) = 5*a(n-1) + 2*a(n-2) - 24*a(n-3). - Colin Barker, Dec 29 2014

E.g.f.: (1/15)*(2*exp(-2*x) - 27*exp(3*x) + 40*exp(4*x)). - G. C. Greubel, Oct 10 2022

Mathematica

LinearRecurrence[{5, 2, -24}, {1, 5, 27}, 41] (* G. C. Greubel, Oct 10 2022 *)
CoefficientList[Series[1/((1+2x)(1-3x)(1-4x)), {x, 0, 40}], x] (* Harvey P. Dale, Oct 28 2022 *)

Prog

(PARI) Vec(1/((1+2*x)*(1-3*x)*(1-4*x)) + O(x^50)) \\ Michel Marcus, Dec 29 2014
(Magma) [(5*2^(2*n+3) +(-1)^n*2^(n+1) -3^(n+3))/15: n in [0..40]]; // G. C. Greubel, Oct 10 2022
(SageMath) [(5*2^(2*n+3) +(-1)^n*2^(n+1) -3^(n+3))/15 for n in range(41)] # G. C. Greubel, Oct 10 2022

Crossrefs

Cf. A016269 for the expansion of 1/((1-2*x)*(1-3*x)*(1-4*x)).

Cf. A249992, A249993, A249994, A249996.

Sequence in context: A202508 A129868 A069993 * A009027 A275540 A037498

Adjacent sequences: A249992 A249993 A249994 * A249996 A249997 A249998

Keyword

nonn,easy

Author

Alex Ratushnyak, Dec 28 2014

Status

approved