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Expansion of (4*x^2+x-1)/(12*x^3+4*x^2+x-1).
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%I #12 Jul 05 2019 16:11:08

%S 1,0,0,12,12,60,252,636,2364,7932,25020,85116,280380,921084,3063996,

%T 10112892,33421884,110641404,365683644,1209311868,3999743292,

%U 13225194492,43735910076,144633607548,478279581756,1581644932860

%N Expansion of (4*x^2+x-1)/(12*x^3+4*x^2+x-1).

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,12).

%F a(n) = a(n-1)+4*a(n-2)+12*a(n-3). G.f.: (4*x^2+x-1)/(12*x^3+4*x^2+x-1). [_Colin Barker_, Nov 02 2012]

%t Clear[M, v, f, g, x, n] M = {{0, 1, 0}, {0, 0, 1}, {12, 4, 1}} v[0] = {1, 0, 0} v[n_] := v[n] = M.v[n - 1] Table[v[n][[1]], {n, 0, 30}]

%t LinearRecurrence[{1,4,12},{1,0,0},40] (* _Harvey P. Dale_, Jul 05 2019 *)

%K nonn,easy

%O 0,4

%A _Roger L. Bagula_ and _Gary W. Adamson_, Nov 14 2008

%E New name from _Colin Barker_ and _Joerg Arndt_, Nov 02 2012