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A020343 Expansion of 1/((1-5x)(1-8x)(1-9x)). 1

%I #12 Sep 08 2022 08:44:45

%S 1,22,327,4100,46781,503202,5201827,52278640,514595961,4986022382,

%T 47721236927,452316244380,4253691236341,39747202125562,

%U 369442770633627,3418759065309320,31519177212527921,289676122850156742

%N Expansion of 1/((1-5x)(1-8x)(1-9x)).

%H Vincenzo Librandi, <a href="/A020343/b020343.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 (22,-157,360).

%F a(n) = 25*5^n/12 -64*8^n/3 +81*9^n/4. - _R. J. Mathar_, Jun 29 2013

%F a(0)=1, a(1)=22, a(3)=327; for n>2, a(n) = 22*a(n-1) -157*a(n-2) +360*a(n-3). - _Vincenzo Librandi_, Jul 03 2013

%F a(n) = 17*a(n-1) -72*a(n-2) +5^n. - _Vincenzo Librandi_, Jul 03 2013

%t CoefficientList[Series[1 / ((1 - 5 x) (1 - 8 x) (1 - 9 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 03 2013 *)

%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-8*x)*(1-9*x)))); /* or */ I:=[1, 22, 327]; [n le 3 select I[n] else 22*Self(n-1)-157*Self(n-2)+360*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 03 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.

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Last modified August 18 18:12 EDT 2024. Contains 375273 sequences. (Running on oeis4.)