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A021129 Expansion of 1/((1-x)(1-2x)(1-5x)(1-8x)). 1

%I #14 Sep 08 2022 08:44:45

%S 1,16,175,1650,14481,122316,1010995,8250550,66817861,538611216,

%T 4329233415,34735589850,278393339641,2229689837716,17850234337435,

%U 142865452943550,1143241514899821,9147521576217816,73188119895363055

%N Expansion of 1/((1-x)(1-2x)(1-5x)(1-8x)).

%H Vincenzo Librandi, <a href="/A021129/b021129.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 (16,-81,146,-80).

%F a(0)=1, a(1)=16, a(2)=175, a(3)=1650; for n>3, a(n) = 16*a(n-1) -81*a(n-2) +146*a(n-3) -80*a(n-4). - _Vincenzo Librandi_, Jul 07 2013

%F a(0)=1, a(1)=16; for n>1, a(n) = 13*a(n-1) -40*a(n-2) +2^n -1. - _Vincenzo Librandi_, Jul 07 2013

%F a(n) = (2*8^(n+3) - 7*5^(n+3) + 14*2^(n+3) - 9)/252. [_Yahia Kahloune_, Jul 07 2013]

%t CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 5 x) (1 - 8 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 07 2013 *)

%t LinearRecurrence[{16,-81,146,-80},{1,16,175,1650},30] (* _Harvey P. Dale_, Nov 12 2021 *)

%o (Magma) I:=[1, 16, 175, 1650]; [n le 4 select I[n] else 16*Self(n-1)-81*Self(n-2)+146*Self(n-3)-80*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-5*x)*(1-8*x)))); // _Vincenzo Librandi_, Jul 07 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.

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Last modified March 28 07:33 EDT 2024. Contains 371235 sequences. (Running on oeis4.)