A360212 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(2*n-5*k,n-3*k).

1, 2, 6, 19, 67, 242, 890, 3310, 12423, 46959, 178526, 681893, 2614698, 10059000, 38807021, 150080294, 581649776, 2258469988, 8783966719, 34214789901, 133450049457, 521134066663, 2037313708685, 7972641631438, 31228124666374, 122421230120657

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Formula

G.f.: 1 / ( sqrt(1-4*x) * (1 + x^3 * c(x)) ), where c(x) is the g.f. of A000108.

D-finite with recurrence 2*n*a(n) +4*(-2*n+1)*a(n-1) +(3*n-4)*a(n-2) +2*(-6*n+11)*a(n-3) +(n-4)*a(n-4) +2*(-n+9)*a(n-5) +4*(-2*n+1)*a(n-6) +(n-4)*a(n-7) +2*(-2*n+9)*a(n-8)=0. - R. J. Mathar, Mar 12 2023

Maple

A360212 := proc(n)
    add((-1)^k*binomial(2*n-5*k, n-3*k), k=0..n/3) ;
end proc:
seq(A360212(n), n=0..70) ; # R. J. Mathar, Mar 12 2023

Prog

(PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(2*n-5*k, n-3*k));
(PARI) my(N=30, x='x+O('x^N)); Vec(1/(sqrt(1-4*x)*(1+2*x^3/(1+sqrt(1-4*x)))))

Crossrefs

Cf. A191993, A307354, A360186.

Cf. A000108, A360152.

Sequence in context: A150094 A305118 A234010 * A121655 A250918 A150095

Adjacent sequences: A360209 A360210 A360211 * A360213 A360214 A360215

Keyword

nonn

Author

Seiichi Manyama, Jan 30 2023

Status

approved