A018070 Expansion of 1/((1-3x)(1-8x)(1-11x)).

1, 22, 339, 4532, 56357, 672210, 7813303, 89300464, 1009144713, 11315328398, 126186563867, 1401795991596, 15529706751469, 171706382611786, 1895807080277631, 20910172869786728, 230462261504563025

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,-145,264).

Formula

a(n) = 22*a(n-1) - 145*a(n-2) + 264*a(n-3) for n>2; a(0)=1, a(1)=22, a(2)=339. - Vincenzo Librandi, Jul 02 2013

a(n) = 19*a(n-1) - 88*a(n-2) + 3^n. - Vincenzo Librandi, Jul 02 2013

a(n) = (5*11^(n+2) - 8^(n+3) + 3^(n+3))/120. - Yahia Kahloune, Jul 06 2013

Mathematica

CoefficientList[Series[1 / ((1 - 3 x) (1 - 8 x) (1 - 11 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 02 2013 *)
LinearRecurrence[{22, -145, 264}, {1, 22, 339}, 30] (* Harvey P. Dale, Jan 22 2014 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-8*x)*(1-11*x)))); /* or */ I:=[1, 22, 339]; [n le 3 select I[n] else 22*Self(n-1)-145*Self(n-2)+264*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 02 2013

Crossrefs

Sequence in context: A018090 A021274 A021534 * A332873 A019490 A021254

Adjacent sequences: A018067 A018068 A018069 * A018071 A018072 A018073

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved