A025971 Expansion of 1/((1-2*x)*(1-4*x)*(1-7*x)*(1-8*x)).

1, 21, 287, 3249, 33159, 317457, 2913079, 25951233, 226266887, 1941258033, 16450020951, 138048250977, 1149556141735, 9512774280849, 78317007130103, 642041894674881, 5244884610706503, 42718957418411505, 347070960515299735, 2813803342053741345, 22771078540971541991

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..900

Index entries for linear recurrences with constant coefficients, signature (21,-154,456,-448).

Formula

a(n) = (5*8^(n+2)-7^(n+3)+10*4^(n+1)-2^(n+1))/15. - Yahia Kahloune, May 23 2013

a(n) = 21*a(n-1)-154*a(n-2)+456*a(n-3)-448*a(n-4), for n >= 4. - Giovanni Resta, May 23 2013

a(n) = (4^(n+1)-2^(n+1))/2+15*a(n-1)-56*a(n-2). - Vincenzo Librandi, Jun 20 2026

Mathematica

CoefficientList[Series[1/((1-2x)(1-4x)(1-7x)(1-8x)), {x, 0, 30}], x] (* Harvey P. Dale, Jun 23 2020 *)

Prog

(Magma) I:=[1, 21]; [n le 2 select I[n] else (4^n-2^n)/2+15*Self(n-1)-56*Self(n-2): n in [1..22]]; // Vincenzo Librandi, Jun 20 2026

Crossrefs

Sequence in context: A296333 A028028 A296633 * A346844 A188710 A304354

Adjacent sequences: A025968 A025969 A025970 * A025972 A025973 A025974

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

a(20) from Vincenzo Librandi, Jun 20 2026

Status

approved