A265037 G.f.: (1 + 22*x - 34*x^2 + 14*x^3)/((1 - x)^2*(1 - 6*x + 8*x^2)).

1, 30, 185, 886, 3855, 16064, 65569, 264930, 1065059, 4270948, 17105253, 68463974, 273941863, 1095939432, 4384101737, 17537095018, 70149756267, 280601777516, 1122412615021, 4489661470062, 17958667900271, 71834715641200, 287338950645105, 1149355978741106

Offset

0,2

Links

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

Physics Forums, How to approximate the rate of growth of an integer sequence? [Contains the sequence of numbers, but not the g.f., which was found by Alexander R. Povolotsky]

Index entries for linear recurrences with constant coefficients, signature (8,-21,22,-8).

Formula

From G. C. Greubel, Feb 26 2017: (Start)

a(n) = 8*a(n-1) - 21*a(n-2) + 22*a(n-3) - 8*a(n-4).

a(n) = (1/12)*(68 + 49*2^(2*n+2) - 63*2^(2 + n) + 12*n).

E.g.f.: (1/12)*(196*exp(4*x) - 252*exp(2*x) + 4*(17 + 3*x)*exp(x)). (End)

Mathematica

CoefficientList[Series[(1 + 22 *x - 34* x^2 + 14 *x^3)/((1 - x)^2 *(1 - 6* x + 8* x^2)), {x, 0, 50}], x] (* G. C. Greubel, Feb 26 2017 *)

Prog

(PARI) x='x+O('x^50); Vec((1 + 22*x - 34*x^2 + 14*x^3)/((1 - x)^2*(1 - 6*x + 8*x^2))) \\ G. C. Greubel, Feb 26 2017

Crossrefs

Sequence in context: A042758 A071311 A337494 * A249001 A249466 A249002

Adjacent sequences: A265034 A265035 A265036 * A265038 A265039 A265040

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 15 2015, based on a suggestion from Alexander R. Povolotsky

Status

approved