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
Keywords
Programs
-
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
-
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)))))
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