A018208 Expansion of 1/((1-3x)(1-11x)(1-12x)).

1, 26, 475, 7520, 110341, 1545446, 20980975, 278565740, 3637529881, 46892529266, 598374287875, 7572794935160, 95188878040621, 1189735265087486, 14798979200433175, 183331466632763780

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (26,-201,396).

Formula

G.f.: 1/((1-3*x)*(1-11*x)*(1-12*x)).

a(0)=1, a(1)=26, a(2)=475; for n>2, a(n) = 26*a(n-1) -201*a(n-2)+396*a(n-3). - Vincenzo Librandi, Jul 02 2013

a(n) = 23*a(n-1) -132*a(n-2) +3^n. - Vincenzo Librandi, Jul 02 2013

a(n) = (8*12^(n+2) - 9*11^(n+2) + 3^(n+2))/72. - Yahia Kahloune, Jul 07 2013

Mathematica

CoefficientList[Series[1 / ((1 - 3 x) (1 - 11 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 02 2013 *)
LinearRecurrence[{26, -201, 396}, {1, 26, 475}, 20] (* Harvey P. Dale, Jul 04 2017 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-11*x)*(1-12*x)))); /* or */ I:=[1, 26, 475]; [n le 3 select I[n] else 26*Self(n-1)-201*Self(n-2)+396*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 02 2013

Crossrefs

Sequence in context: A019747 A163740 A021334 * A240190 A001723 A163201

Adjacent sequences: A018205 A018206 A018207 * A018209 A018210 A018211

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved