A021064 - OEIS

%I #28 Jan 27 2025 14:42:27

%S 1,18,241,2982,36085,433986,5210857,62539614,750503869,9006132954,

%T 108073857073,1296887073846,15562647261253,186751774276722,

%U 2241021312778489,26892255817780878,322707070006818637,3872484840662430090,46469818089691504705,557637817081526135910,6691653804993999966421

%N Expansion of 1/((1-x)*(1-2*x)*(1-3*x)*(1-12*x)).

%H Vincenzo Librandi, <a href="/A021064/b021064.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 (18,-83,138,-72).

%F From _Vincenzo Librandi_, Jul 05 2013: (Start)

%F a(0)=1, a(1)=18; for n>1, a(n)= 15*a(n-1) -36*a(n-2) + 2^n - 1.

%F a(0)=1, a(1)=18, a(2)=241, a(3)=2982; for n>3, a(n) = 18*a(n-1) -83*a(n-2) +138*a(n-3) -72*a(n-4). (End)

%F a(n) = (12^(n+3) - 55*3^(n+3) + 99*2^(n+3) - 45)/990. [_Yahia Kahloune_, Jul 07 2013]

%t CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 3 x) (1 - 12 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 05 2013 *)

%t LinearRecurrence[{18,-83,138,-72},{1,18,241,2982},30] (* _Harvey P. Dale_, Jan 26 2025 *)

%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-3*x)*(1-12*x)))); // _Vincenzo Librandi_, Jul 05 2013

%o (Magma) I:=[1, 18, 241, 2982]; [n le 4 select I[n] else 18*Self(n-1)-83*Self(n-2)+138*Self(n-3)-72*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 05 2013

%K nonn,easy,changed

%O 0,2

%A _N. J. A. Sloane_