A017065 Expansion of 1/((1-3x)(1-4x)(1-11x)).

1, 18, 235, 2760, 31141, 345918, 3819295, 42071220, 463025881, 5094274218, 56041033555, 616467614880, 6781209278221, 74593565712918, 820530282235015, 9025837356505740, 99284227972292161, 1092126576027270018

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (18,-89,132).

Formula

a(n) = 9*3^n/8 - 16*4^n/7 + 121*11^n/56. - R. J. Mathar, Jun 23 2013

From Vincenzo Librandi, Jun 26 2013: (Start)

a(n) = 18*a(n-1) - 89*a(n-2) + 132*a(n-3).

a(n) = 15*a(n-1) - 44*a(n-2) + 3^n. (End)

Mathematica

CoefficientList[Series[1 / ((1 - 3 x) (1 - 4 x) (1 - 11 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jun 26 2013 *)
LinearRecurrence[{18, -89, 132}, {1, 18, 235}, 20] (* Harvey P. Dale, Jul 28 2023 *)

Prog

(Magma) I:=[1, 18, 235]; [n le 3 select I[n] else 18*Self(n-1)-89*Self(n-2)+132*Self(n-3): n in [1..20]]; /* or */ m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-4*x)*(1-11*x)))); // Vincenzo Librandi, Jun 26 2013
(PARI) x='x+O('x^20); Vec(1/((1-3*x)*(1-4*x)*(1-11*x))) \\ Altug Alkan, Sep 23 2018

Crossrefs

Sequence in context: A275963 A125453 A016256 * A016252 A016301 A058126

Adjacent sequences: A017062 A017063 A017064 * A017066 A017067 A017068

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved