A021134 - OEIS

%I #19 Nov 20 2024 14:10:49

%S 1,17,200,2050,19731,184047,1688890,15362600,139076861,1255760077,

%T 11322184380,102001381950,918521058391,8269232646107,74435809450670,

%U 669985863300100,6030190661052321,54273305406490137

%N Expansion of 1/((1-x)*(1-2*x)*(1-5*x)*(1-9*x)).

%H Vincenzo Librandi, <a href="/A021134/b021134.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 (17,-89,163,-90).

%F a(0)=1, a(1)=17; for n>1, a(n) = 14*a(n-1) -45*a(n-2) +2^n -1. - _Vincenzo Librandi_, Jul 07 2013

%F a(0)=1, a(1)=17, a(2)=200, a(3)=2050; for n>3, a(n) = 17*a(n-1) -89*a(n-2) +163*a(n-3) -90*a(n-4). - _Vincenzo Librandi_, Jul 07 2013

%F a(n) = (3*9^(n+3) - 14*5^(n+3) +32*2^(n+3) - 21)/672. [_Yahia Kahloune_, Jul 07 2013]

%t CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 5 x) (1 -  9 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 07 2013 *)

%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-5*x)*(1-9*x)))); // _Vincenzo Librandi_, Jul 07 2013

%o (Magma) I:=[1, 17, 200, 2050]; [n le 4 select I[n] else 17*Self(n-1)-89*Self(n-2)+163*Self(n-3)-90*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 07 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_