A017953 Expansion of 1/((1-3x)(1-6x)(1-11x)).

1, 20, 283, 3518, 41209, 468608, 5247271, 58277666, 644406997, 7108612676, 78315612739, 862197157094, 9488521761265, 104399859167624, 1148555174389087, 12635047273900202, 138991162189670413

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (20,-117,198).

Formula

a(0)=1, a(1)=20, a(2)=283; for n>2, a(n) = 20*a(n-1) -117*a(n-2) +198*a(n-3). - Vincenzo Librandi, Jul 02 2013

a(n) = 17*a(n-1) -66*a(n-2) +3^n. - Vincenzo Librandi, Jul 02 2013

a(n) = (3*11^(n+2) - 8*6^(n+2) + 5*3^(n+2))/120. [Yahia Kahloune, Jul 06 2013]

Mathematica

CoefficientList[Series[1 / ((1 - 3 x) (1 - 6 x) (1 - 11 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 02 2013 *)
LinearRecurrence[{20, -117, 198}, {1, 20, 283}, 30] (* Harvey P. Dale, Aug 31 2020 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-6*x)*(1-11*x)))); /* or */ I:=[1, 20, 283]; [n le 3 select I[n] else 20*Self(n-1)-117*Self(n-2)+198*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 02 2013

Crossrefs

Sequence in context: A278360 A019040 A021204 * A016317 A021404 A046175

Adjacent sequences: A017950 A017951 A017952 * A017954 A017955 A017956

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved