A021092 - OEIS

A021092

Expansion of 1/((1-x)*(1-2*x)*(1-4*x)*(1-10*x)).

1, 17, 205, 2205, 22701, 229677, 2307565, 23119085, 231365101, 2314349037, 23146284525, 231474025965, 2314784990701, 23148028847597, 231481004271085, 2314812905956845, 23148140512683501, 231481450939557357, 2314814692646987245, 23148147659476575725, 231481479526794667501

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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,-84,148,-80).

FORMULA

a(n) = -(1/27)+(1/2)*2^n-(16/9)*4^n+(125/54)*10^n. - Antonio Alberto Olivares, May 22 2012

a(0)=1, a(1)=17; for n>1, a(n) = 14*a(n-1) -40*a(n-2) +2^n - 1. - Vincenzo Librandi, Jul 06 2013

a(0)=1, a(1)=17, a(2)=205, a(3)=2205; for n>3, a(n) = 17*a(n-1) -84*a(n-2) +148*a(n-3) -80*a(n-4). - Vincenzo Librandi, Jul 06 2013

MATHEMATICA

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 4 x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 06 2013 *)

PROG

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-4*x)*(1-10*x)))); // Vincenzo Librandi, Jul 06 2013

(Magma) I:=[1, 17, 205, 2205]; [n le 4 select I[n] else 17*Self(n-1)-84*Self(n-2)+148*Self(n-3)-80*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 06 2013

CROSSREFS

First differences of A016292.

Sequence in context: A016311 A140961 A016306 * A219124 A383945 A246989

Adjacent sequences: A021089 A021090 A021091 * A021093 A021094 A021095

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved