A114749 a(n) = a(n-1) + 4*a(n-2) + 6*a(n-3) + 4*a(n-4) + a(n-5).

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, 9030048595141

Offset: 0

Author

Roger L. Bagula, Feb 18 2006

Keywords

• nonn
• easy
• changed

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,4,6,4,1).

Crossrefs

Cf. A107479, A107480, A109538, A109543, A109544, A125950, A130844, A143335, A147851.

Programs

Magma

m:=50; R:=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

Mathematica

LinearRecurrence[{1,4,6,4,1},{0,1,1,2,3},30] (* Harvey P. Dale, Oct 13 2011 *)

PARI

my(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

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