A024170 Expansion of 1/((1-x)(1-6x)(1-9x)(1-10x)).

1, 26, 447, 6412, 83153, 1012158, 11803219, 133502864, 1476280245, 16046160130, 172084379831, 1825884161556, 19206817023577, 200615621740742, 2083177317949083, 21525527306347288, 221502445537069949

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (26,-229,744,-540).

Formula

a(n) = (120*10^(n+3) - 180*9^(n+3) + 72*6^(n+3) - 12)/4320. [Yahia Kahloune, Jun 28 2013]

a(0)=1, a(1)=26, a(2)=447, a(3)=6412; for n>3, a(n) = 26*a(n-1) -229*a(n-2) +744*a(n-3) -540*a(n-4). - Vincenzo Librandi, Jul 16 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 6 x) (1 - 9 x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 16 2013 *)
LinearRecurrence[{26, -229, 744, -540}, {1, 26, 447, 6412}, 30] (* Harvey P. Dale, Jul 18 2013 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-6*x)*(1-9*x)*(1-10*x)))); /* or */  I:=[1, 26, 447, 6412]; [n le 4 select I[n] else 26*Self(n-1)-229*Self(n-2)+744*Self(n-3)-540*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 16 2013

Crossrefs

Sequence in context: A025999 A028058 A331881 * A028042 A023956 A025981

Adjacent sequences: A024167 A024168 A024169 * A024171 A024172 A024173

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved