A249997 Expansion of 1/((1-x)*(1+3*x)*(1-4*x)).

1, 2, 15, 40, 221, 702, 3355, 11780, 52041, 193402, 817895, 3138720, 12953461, 50618102, 206059635, 813476860, 3286192481, 13047914802, 52482224575, 209057202200, 838843897101, 3347530323502, 13413657088715, 53584020970740, 214547906035321, 857556157684202

Offset: 0

Author

Alex Ratushnyak, Dec 28 2014

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 (2,11,-12).

Crossrefs

Cf. A016208, A099621, A249998, A249999.

Programs

Magma

[((-1)^n*3^(n+3) +4^(n+3) -7)/84: n in [0..50]]; // G. C. Greubel, Jul 21 2022

Mathematica

LinearRecurrence[{2,11,-12}, {1,2,15}, 50] (* G. C. Greubel, Jul 21 2022 *)

SageMath

[((-1)^n*3^(n+3) +4^(n+3) -7)/84 for n in (0..50)] # G. C. Greubel, Jul 21 2022

Formula

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

a(n) = (-1)^n*3^(n+2)/28 + 4^(n+2)/21 -1/12. - R. J. Mathar, Jan 09 2015

E.g.f.: (1/84)*(27*exp(-3*x) - 7*exp(x) + 64*exp(4*x)). - G. C. Greubel, Jul 21 2022