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A114749
a(n) = a(n-1) + 4*a(n-2) + 6*a(n-3) + 4*a(n-4) + a(n-5).
9
0, 1, 1, 2, 3, 21, 50, 161, 501, 1532, 4723, 14551, 44800, 137971, 424901, 1308512, 4029693, 12409831, 38217250, 117693681, 362448951, 1116196192, 3437432913, 10585903361, 32600301650, 100395746291, 309178300901, 952144142322, 2932218933633
OFFSET
0,4
FORMULA
G.f.: x*(9*x^3 + 3*x^2 - 1)/((x^2 + x + 1)*(x^3 + 3*x^2 + 2*x - 1)). [Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009]
MATHEMATICA
LinearRecurrence[{1, 4, 6, 4, 1}, {0, 1, 1, 2, 3}, 30] (* Harvey P. Dale, Oct 13 2011 *)
PROG
(PARI) x='x+O('x^50); concat([0], Vec(x*(9*x^3+3*x^2-1)/((x^2+x+1)*(x^3+ 3*x^2+2*x-1)))) \\ G. C. Greubel, Nov 03 2018
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(x*(9*x^3+3*x^2-1)/((x^2+x+1)*(x^3+ 3*x^2+2*x-1)))); // G. C. Greubel, Nov 03 2018
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Feb 18 2006
STATUS
approved