A021184 Expansion of 1/((1-x)(1-2x)(1-6x)(1-8x)).

1, 17, 197, 1957, 17973, 157749, 1345909, 11271029, 93191285, 763669621, 6218195061, 50398593141, 407106949237, 3280364834933, 26383974158453, 211918126207093, 1700423007424629, 13633852046266485, 109253624291872885

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (17,-92,172,-96).

Formula

a(n) = (10*8^(n+3) - 21*6^(n+3) + 35*2^(n+3) - 24)/840. [Yahia Kahloune, Jul 05 2013]

a(0)=1, a(1)=17; for n>1, a(n) = 14*a(n-1) -48*a(n-2) +2^n -1. - Vincenzo Librandi, Jul 07 2013

a(0)=1, a(1)=17, a(2)=197, a(3)=1957; for n>3, a(n) = 17*a(n-1) -92*a(n-2) +172*a(n-3) -96*a(n-4). - Vincenzo Librandi, Jul 07 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 6 x) (1 -  8 x)), {x, 0, 20}], x]  (* Vincenzo Librandi, Jul 07 2013 *)
LinearRecurrence[{17, -92, 172, -96}, {1, 17, 197, 1957}, 30] (* Harvey P. Dale, Jul 17 2015 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-6*x)*(1-8*x)))); /* or */ I:=[1, 17, 197, 1957]; [n le 4 select I[n] else 17*Self(n-1)-92*Self(n-2)+172*Self(n-3)-96*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 07 2013

Crossrefs

Sequence in context: A262111 A238672 A018250 * A069361 A177135 A130817

Adjacent sequences: A021181 A021182 A021183 * A021185 A021186 A021187

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved