A023949 Expansion of 1/((1-x)(1-6x)(1-7x)(1-8x)).

1, 22, 317, 3782, 40533, 405534, 3869149, 35663254, 320292005, 2819331086, 24426173421, 208945416966, 1768927681717, 14848644708478, 123763757447933, 1025496480025718, 8455062115190469, 69418440837750510

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (22,-167,482,-336).

Formula

a(n) = (30*8^(n+3) - 10*7^(n+4) + 7*6^(n+4) - 2)/420. [Yahia Kahloune, Jun 27 2013]

a(0)=1, a(1)=22, a(2)=317, a(3)=3782; for n>3, a(n) = 22*a(n-1) -167*a(n-2) +482*a(n-3) -336*a(n-4). - Vincenzo Librandi, Jul 12 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 6 x) (1 - 7 x) (1 - 8 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 12 2013 *)

Prog

(Magma) I:=[1, 22, 317, 3782]; [n le 4 select I[n] else 22*Self(n-1)-167*Self(n-2)+482*Self(n-3)-336*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-6*x)*(1-7*x)*(1-8*x)))); // Vincenzo Librandi, Jul 12 2013

Crossrefs

Sequence in context: A326277 A025988 A267132 * A025972 A028029 A022453

Adjacent sequences: A023946 A023947 A023948 * A023950 A023951 A023952

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved