A024170 - OEIS

%I #25 Dec 11 2024 06:39:26

%S 1,26,447,6412,83153,1012158,11803219,133502864,1476280245,

%T 16046160130,172084379831,1825884161556,19206817023577,

%U 200615621740742,2083177317949083,21525527306347288,221502445537069949

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

%H Vincenzo Librandi, <a href="/A024170/b024170.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (26,-229,744,-540).

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

%F 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

%t CoefficientList[Series[1 / ((1 - x) (1 - 6 x) (1 - 9 x) (1 - 10 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 16 2013 *)

%t LinearRecurrence[{26,-229,744,-540},{1,26,447,6412},30] (* _Harvey P. Dale_, Jul 18 2013 *)

%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-6*x)*(1-9*x)*(1-10*x)))); // _Vincenzo Librandi_, Jul 16 2013

%o (Magma) 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

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_