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%I #18 Mar 01 2023 14:24:11
%S 1,22,333,4334,52325,606606,6874477,76908238,854115189,9445967630,
%T 104219612861,1148348383182,12643672205893,139152654913294,
%U 1531118871452685,16844976107996366,185310900907951637,2038517655246870798,22424284493969261149,246670690224670294990
%N Expansion of 1/((1-5x)(1-6x)(1-11x)).
%H Vincenzo Librandi, <a href="/A019854/b019854.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 (22,-151,330).
%F G.f.: 1/((1-5*x)*(1-6*x)*(1-11*x)).
%F a(n) = 25*5^n/6 -36*6^n/5 +121*11^n/30. - _R. J. Mathar_, Jun 29 2013
%F a(0)=1, a(1)=22, a(2)=333; for n>2, a(n) = 22*a(n-1) -151*a(n-2) +330*a(n-3). - _Vincenzo Librandi_, Jul 03 2013
%F a(n)= 17*a(n-1) -66*a(n-2) +5^n. - _Vincenzo Librandi_, Jul 03 2013
%p a:= n-> (Matrix(3, (i, j)-> `if`(i=j-1, 1, `if`(j=1, [22, -151, 330][i], 0)))^n)[1, 1]: seq(a(n), n=0..25); # _Alois P. Heinz_, Jul 03 2013
%t CoefficientList[Series[1 / ((1 - 5 x) (1 - 6 x) (1 - 11 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 03 2013 *)
%t LinearRecurrence[{22,-151,330},{1,22,333},30] (* _Harvey P. Dale_, Nov 17 2014 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-6*x)*(1-11*x)))); /* or */ I:=[1, 22, 333]; [n le 3 select I[n] else 22*Self(n-1)-151*Self(n-2)+330*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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