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Expansion of 1/((1-5x)(1-11x)(1-12x)).
1

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

%S 1,28,537,8780,131681,1872828,25708777,344166700,4522666161,

%T 58593270428,750663052217,9530987332620,120125429898241,

%U 1504795780456828,18753752307454857,232703290568738540

%N Expansion of 1/((1-5x)(1-11x)(1-12x)).

%H Vincenzo Librandi, <a href="/A020569/b020569.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (28,-247,660).

%F a(n) = 25*5^n/42 -121*11^n/6 +144*12^n/7. - _R. J. Mathar_, Jun 30 2013

%F a(0)=1, a(1)=28, a(2)=537; for n>2, a(n) = 28*a(n-1) -247*a(n-2) +660*a(n-3). - _Vincenzo Librandi_, Jul 04 2013

%F a(n) = 23*a(n-1) -132*a(n-2) +5^n. - _Vincenzo Librandi_, Jul 04 2013

%t CoefficientList[Series[1 / ((1 - 5 x) (1 - 11 x) (1 - 12 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 04 2013 *)

%t LinearRecurrence[{28,-247,660},{1,28,537},20] (* _Harvey P. Dale_, Dec 25 2013 *)

%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-11*x)*(1-12*x)))); /* or */ I:=[1, 28, 537]; [n le 3 select I[n] else 28*Self(n-1)-247*Self(n-2)+660*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 04 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.