A021503 Expansion of 1/((1-x)(1-3x)(1-6x)(1-8x)).

1, 18, 217, 2214, 20701, 183906, 1582129, 13325598, 110626021, 909165114, 7418351161, 60217256502, 486961532461, 3927035533842, 31604351090113, 253963231160526, 2038476448492021, 16348435376893290

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,-107,234,-144).

Formula

a(n) = (3*8^(n+3)-7*6^(n+3)+7*3^(n+3)-3)/210. - Yahia Kahloune, May 06 2013

a(0)=1, a(1)=18; for n>1, a(n) = 14*a(n-1) -48*a(n-2) +(3^n -1)/2. - Vincenzo Librandi, Jul 10 2013

a(0)=1, a(1)=18, a(2)=217, a(3)=2214; for n>3, a(n) = 18*a(n-1) -107*a(n-2) +234*a(n-3) -144*a(n-4). - Vincenzo Librandi, Jul 10 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 3 x)(1 - 6 x) (1 - 8 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 10 2013 *)
LinearRecurrence[{18, -107, 234, -144}, {1, 18, 217, 2214}, 20] (* Harvey P. Dale, Mar 05 2022 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-6*x)*(1-8*x)))); /* or */ I:=[1, 18, 217, 2214]; [n le 4 select I[n] else 18*Self(n-1)-107*Self(n-2)+234*Self(n-3)-144*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 10 2013

Crossrefs

Sequence in context: A081136 A101188 A019757 * A025470 A046915 A041616

Adjacent sequences: A021500 A021501 A021502 * A021504 A021505 A021506

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved