A021064 Expansion of 1/((1-x)(1-2x)(1-3x)(1-12x)).

1, 18, 241, 2982, 36085, 433986, 5210857, 62539614, 750503869, 9006132954, 108073857073, 1296887073846, 15562647261253, 186751774276722, 2241021312778489, 26892255817780878, 322707070006818637

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,-83,138,-72).

Formula

a(0)=1, a(1)=18; for n>1, a(n)= 15*a(n-1) -36*a(n-2) + 2^n - 1. - Vincenzo Librandi, Jul 05 2013

a(0)=1, a(1)=18, a(2)=241, a(3)=2982; for n>3, a(n) = 18*a(n-1) -83*a(n-2) +138*a(n-3) -72*a(n-4). - Vincenzo Librandi, Jul 05 2013

a(n) = (12^(n+3) - 55*3^(n+3) + 99*2^(n+3) - 45)/990. [Yahia Kahloune, Jul 07 2013]

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 3 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 05 2013 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-3*x)*(1-12*x)))); /* or */ I:=[1, 18, 241, 2982]; [n le 4 select I[n] else 18*Self(n-1)-83*Self(n-2)+138*Self(n-3)-72*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 05 2013

Crossrefs

Sequence in context: A016301 A058126 A016247 * A181379 A080629 A053540

Adjacent sequences: A021061 A021062 A021063 * A021065 A021066 A021067

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved