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A021394 Expansion of 1/((1-x)(1-3x)(1-4x)(1-11x)). 1

%I #17 Sep 08 2022 08:44:45

%S 1,19,254,3014,34155,380073,4199368,46270588,509296469,5603570687,

%T 61644604242,678112219122,7459321497343,82052887210261,

%U 902583169445276,9928420525951016,109212648498243177,1201339224525513195

%N Expansion of 1/((1-x)(1-3x)(1-4x)(1-11x)).

%H Vincenzo Librandi, <a href="/A021394/b021394.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (19,-107,221,-132).

%F a(0)=1, a(1)=19; for n>1, a(n) = 15*a(n-1) -44*a(n-2) +(3^n-1)/2. - _Vincenzo Librandi_, Jul 09 2013

%F a(0)=1, a(1)=19, a(2)=254, a(3)=3014; for n>3, a(n) = 19*a(n-1) -107*a(n-2) +221*a(n-3) -132*a(n-4). - _Vincenzo Librandi_, Jul 09 2013

%F a(n) = (3*11^(n+3) - 80*4^(n+3) + 105*3^(n+3) - 28)/1680. [_Yahia Kahloune_, Aug 12 2013]

%p A021394:=n->(3*11^(n+3) - 80*4^(n+3) + 105*3^(n+3) - 28)/1680; seq(A021394(n), n=0..100); # _Wesley Ivan Hurt_, Nov 11 2013

%t CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 4 x) (1 - 11 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 09 2013 *)

%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-4*x)*(1-11*x)))); /* or */ I:=[1, 19, 254, 3014]; [n le 4 select I[n] else 19*Self(n-1)-107*Self(n-2)+221*Self(n-3)-132*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 09 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.

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Last modified March 28 15:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)