A021034 Expansion of 1/((1-x)*(1-2*x)*(1-3*x)*(1-7*x)).

1, 13, 116, 902, 6615, 47271, 333922, 2346784, 16455989, 115278449, 807210768, 5651264346, 39561225523, 276935720347, 1938571500254, 13570064940788, 94990648033617, 664935116841765, 4654547560235980

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (13,-53,83,-42).

Formula

a(0)=1, a(1)=13; for n>1, a(n) = 10*a(n-1) -21*a(n-2) +2^n -1. - Vincenzo Librandi, Jul 05 2013

a(0)=1, a(1)=13, a(2)=116, a(3)=902; for n>3, a(n) = 13*a(n-1) -53*a(n-2) +83*a(n-3) -42*a(n-4). - Vincenzo Librandi, Jul 05 2013

a(n) = (7^(n+3) - 15*3^(n+3) + 24*2^(n+3) - 10)/120. [Yahia Kahloune, Jul 07 2013]

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 3 x) (1 - 7 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 05 2013 *)
LinearRecurrence[{13, -53, 83, -42}, {1, 13, 116, 902}, 30] (* Harvey P. Dale, Oct 01 2014 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-3*x)*(1-7*x)))); // Vincenzo Librandi, Jul 05 2013
(Magma) I:=[1, 13, 116, 902]; [n le 4 select I[n] else 13*Self(n-1)-53*Self(n-2)+83*Self(n-3)-42*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 05 2013

Crossrefs

Sequence in context: A376153 A232319 A296332 * A296632 A250316 A250557

Adjacent sequences: A021031 A021032 A021033 * A021035 A021036 A021037

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved