A021274 Expansion of g.f. 1/((1 - x)*(1 - 2*x)*(1 - 8*x)*(1 - 11*x)).

1, 22, 337, 4482, 55533, 660774, 7667929, 87542794, 988535845, 11078416206, 123498755601, 1371575734386, 15192048468637, 167950256294518, 1854154604388553, 20449314929530458, 225371378475017109, 2482516477226906910, 27335131761510249985, 300906053472727990210, 3311723420968931912461

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,-147,302,-176).

Formula

a(n) = (7*11^(n+3) - 15*8^(n+3) + 35*2^(n+3) - 27)/1890. - Yahia Kahloune, Jul 08 2013

a(0)=1, a(1)=22, a(2)=337, a(3)=4482; for n>3, a(n) = 22*a(n-1) -147*a(n-2) +302*a(n-3)-176*a(n-4). - Vincenzo Librandi, Jul 08 2013

a(0)=1, a(1)=22; for n>1, a(n) = 19*a(n-1) -88*a(n-2) +2^n -1. - Vincenzo Librandi, Jul 08 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 8 x) (1 - 11 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 08 2013 *)
LinearRecurrence[{22, -147, 302, -176}, {1, 22, 337, 4482}, 20] (* Harvey P. Dale, Jun 09 2017 *)

Prog

(Magma) I:=[1, 22, 337, 4482]; [n le 4 select I[n] else 22*Self(n-1)-147*Self(n-2)+302*Self(n-3)-176*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 08 2013
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-8*x)*(1-11*x)))); // Vincenzo Librandi, Jul 08 2013

Crossrefs

Sequence in context: A348134 A223812 A018090 * A021534 A018070 A332873

Adjacent sequences: A021271 A021272 A021273 * A021275 A021276 A021277

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved