A021229 Expansion of 1/((1-x)(1-2x)(1-7x)(1-9x)).

1, 19, 248, 2786, 28983, 288273, 2786566, 26424112, 247232645, 2291004287, 21080414004, 192953358078, 1759187655187, 15990940940461, 145026232803362, 1312990445670284, 11871194464243809, 107220713350935195

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (19,-113,221,-126).

Formula

a(n) = (15*9^(n+3) - 28*7^(n+3) + 48*2^(n+3) - 35)/1680. - Yahia Kahloune, May 19 2013

a(0)=1, a(1)=19, a(2)=248, a(3)=2786; for n>3, a(n) = 19*a(n-1) -113*a(n-2) +221*a(n-3) -126*a(n-4). - Vincenzo Librandi, Jul 08 2013

a(0)=1, a(1)=19; for n>1, a(n) = 16*a(n-1) -63*a(n-2) +2^n -1. - Vincenzo Librandi, Jul 08 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 7 x) (1 - 9 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 08 2013 *)
LinearRecurrence[{19, -113, 221, -126}, {1, 19, 248, 2786}, 20]

Prog

(Magma) I:=[1, 19, 248, 2786]; [n le 4 select I[n] else 19*Self(n-1)-113*Self(n-2)+221*Self(n-3)-126*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-7*x)*(1-9*x)))); // Vincenzo Librandi, Jul 08 2013

Crossrefs

Sequence in context: A224180 A318194 A019443 * A021464 A017998 A018912

Adjacent sequences: A021226 A021227 A021228 * A021230 A021231 A021232

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved