A390591 - OEIS

A390591

a(n) = Sum_{k=0..n} (-1)^k * binomial(3*n-k+4,n-k).

1, 6, 37, 230, 1444, 9142, 58277, 373596, 2406241, 15559016, 100942636, 656768216, 4283802832, 28002175286, 183395014053, 1203160693752, 7905359319187, 52013336790742, 342646048673597, 2259775294651342, 14918679053419472, 98583341240894632, 652006213595945132

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OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: g^4/((1-3*x*g^2) * (1+x*g^2)) where g = 1+x*g^3 is the g.f. of A001764.

a(n) = Sum_{k=0..n} (-2)^k * binomial(3*n+5,n-k).

a(n) = Sum_{k=0..n} (-1)^k * 2^(n-k) * binomial(3*n+5,k) * binomial(3*n-k+4,n-k).

a(n) = Sum_{k=0..floor(n/2)} binomial(3*n-2*k+3,n-2*k).

PROG

(PARI) a(n) = sum(k=0, n, (-1)^k*binomial(3*n-k+4, n-k));