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A021034 Expansion of 1/((1-x)(1-2x)(1-3x)(1-7x)). 1

%I #16 Sep 08 2022 08:44:45

%S 1,13,116,902,6615,47271,333922,2346784,16455989,115278449,807210768,

%T 5651264346,39561225523,276935720347,1938571500254,13570064940788,

%U 94990648033617,664935116841765,4654547560235980

%N Expansion of 1/((1-x)(1-2x)(1-3x)(1-7x)).

%H Vincenzo Librandi, <a href="/A021034/b021034.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 (13,-53,83,-42).

%F a(0)=1, a(1)=13; for n>1, a(n) = 10*a(n-1) -21*a(n-2) +2^n -1. - _Vincenzo Librandi_, Jul 05 2013

%F a(0)=1, a(1)=13, a(2)=116, a(3)=902; for n>3, a(n) = 13*a(n-1) -53*a(n-2) +83*a(n-3) -42*a(n-4). - _Vincenzo Librandi_, Jul 05 2013

%F a(n) = (7^(n+3) - 15*3^(n+3) + 24*2^(n+3) - 10)/120. [_Yahia Kahloune_, Jul 07 2013]

%t CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 3 x) (1 - 7 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 05 2013 *)

%t LinearRecurrence[{13,-53,83,-42},{1,13,116,902},30] (* _Harvey P. Dale_, Oct 01 2014 *)

%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-3*x)*(1-7*x)))); /* or */ I:=[1, 13, 116, 902]; [n le 4 select I[n] else 13*Self(n-1)-53*Self(n-2)+83*Self(n-3)-42*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 05 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)