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A020571 Expansion of 1/((1-6x)(1-7x)(1-9x)). 1

%I

%S 1,22,325,4030,45301,478702,4851925,47752510,460048501,4362445582,

%T 40876539925,379553364190,3499808594101,32098136255662,

%U 293160602826325,2668857246099070,24235419069434101,219645625266148942

%N Expansion of 1/((1-6x)(1-7x)(1-9x)).

%H Vincenzo Librandi, <a href="/A020571/b020571.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,-159,378).

%F a(n) = 12*6^n -49*7^n/2 +27*9^n/2. - _R. J. Mathar_, Jun 30 2013

%F a(0)=1, a(1)=22, a(2)=325; for n>2, a(n) = 22*a(n-1) -159*a(n-2) +378*a(n-3). - _Vincenzo Librandi_, Jul 04 2013

%F a(n) = 16*a(n-1) -63*a(n-2) +6^n. - _Vincenzo Librandi_, Jul 04 2013

%t CoefficientList[Series[1 / ((1 - 6 x) (1 - 7 x) (1 - 9 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 04 2013 *)

%t LinearRecurrence[{22,-159,378},{1,22,325},30] (* _Harvey P. Dale_, Dec 11 2018 *)

%o (MAGMA) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-6*x)*(1-7*x)*(1-9*x)))); /* or */ I:=[1, 22, 325]; [n le 3 select I[n] else 22*Self(n-1)-159*Self(n-2)+378*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 June 1 02:09 EDT 2020. Contains 334758 sequences. (Running on oeis4.)