A021076 Expansion of 1/((1-x)(1-2x)(1-4x)(1-6x)).

1, 13, 113, 833, 5649, 36561, 230161, 1424401, 8720657, 53021969, 320925969, 1936736529, 11665150225, 70169841937, 421734846737, 2533272326417, 15211087073553, 91312335163665, 548057262395665

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,-56,92,-48).

Formula

a(n) = -(1/15)+2^n-(16/3)*4^n+(27/5)*6^n. [Antonio Alberto Olivares, May 22 2012]

a(0)=1, a(1)=13, a(2)=113, a(3)=833, a(n)=13*a(n-1)-56*a(n-2)+ 92*a(n-3)- 48*a(n-4) From Harvey P. Dale, Jul 19 2012

a(0)=1, a(1)=13; for n>1, a(n) = 10*a(n-1) -24*a(n-2) +2^n -1. - Vincenzo Librandi, Jul 05 2013

Mathematica

CoefficientList[Series[1/((1-x)(1-2x)(1-4x)(1-6x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{13, -56, 92, -48}, {1, 13, 113, 833}, 30] (* Harvey P. Dale, Jul 19 2012 *)

Prog

(Maxima) a(n):=-(1/15)+2^n-(16/3)*4^n+(27/5)*6^n$ makelist(a(n), n, 0, 18); /* Antonio Alberto Olivares, May 22 2012 */
(Magma) I:=[1, 13]; [n le 2 select I[n] else 10*Self(n-1)-24*Self(n-2)+2^n-1: n in [1..25]]; // Vincenzo Librandi, Jul 05 2013
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-4*x)*(1-6*x)))); // Vincenzo Librandi, Jul 05 2013

Crossrefs

Sequence in context: A182022 A211846 A196862 * A125376 A048545 A164609

Adjacent sequences: A021073 A021074 A021075 * A021077 A021078 A021079

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved