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 A020579 Expansion of 1/((1-6x)(1-8x)(1-9x)). 1

%I

%S 1,23,355,4595,53851,592403,6240235,63710915,635468251,6225852083,

%T 60146237515,574587484835,5439634923451,51116555484563,

%U 477406092913195,4435981769620355,41041272503703451,378327871809737843

%N Expansion of 1/((1-6x)(1-8x)(1-9x)).

%H Vincenzo Librandi, <a href="/A020579/b020579.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 (23,-174,432).

%F a(n) = 6*6^n -32*8^n +27*9^n. - _R. J. Mathar_, Jun 30 2013

%F a(0)=1, a(1)=23, a(2)=355; for n>2, a(n) = 23*a(n-1) -174*a(n-2) +432*a(n-3). - _Vincenzo Librandi_, Jul 04 2013

%F a(n) = 17*a(n-1) -72*a(n-2) +6^n. - _Vincenzo Librandi_, Jul 04 2013

%t CoefficientList[Series[1 / ((1 - 6 x) (1 - 8 x) (1 - 9 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 04 2013 *)

%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-6*x)*(1-8*x)*(1-9*x)))); /* or */ I:=[1,23,355]; [n le 3 select I[n] else 23*Self(n-1)-174*Self(n-2)+432*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 04 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.

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Last modified January 29 10:55 EST 2023. Contains 359922 sequences. (Running on oeis4.)