A021629 Expansion of 1/((1-x)*(1-3*x)*(1-7*x)*(1-12*x)).

1, 23, 366, 5062, 65555, 820701, 10087792, 122732444, 1484551749, 17896987459, 215340503378, 2588122883346, 31085733296983, 373226612833097, 4480104054056724, 53770941570620968, 645319149365603657, 7744304746208018415, 92934981631822773430, 1115243052324902540510

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (23,-163,393,-252).

Formula

a(0)=1, a(1)=23, a(2)=366, a(3)=5062; for n>3, a(n) = 23*a(n-1) -163*a(n-2) +393*a(n-3) -252*a(n-4). - Vincenzo Librandi, Jul 11 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 7 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 11 2013 *)
LinearRecurrence[{23, -163, 393, -252}, {1, 23, 366, 5062}, 30] (* Harvey P. Dale, Aug 09 2015 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-7*x)*(1-12*x)))); // Vincenzo Librandi, Jul 11 2013
(Magma) I:=[1, 23, 366, 5062]; [n le 4 select I[n] else 23*Self(n-1)-163*Self(n-2)+393*Self(n-3)-252*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 11 2013

Crossrefs

Sequence in context: A019682 A021844 A019672 * A019869 A021294 A019628

Adjacent sequences: A021626 A021627 A021628 * A021630 A021631 A021632

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved