OFFSET
0,2
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..n} 9^k * binomial(n/3+1/3,k) * binomial(n-1,n-k).
D-finite with recurrence n*(n-1)*(n+1)*a(n) -8*(2*n-5)*(8*n^2-40*n+57)*a(n-3) +4096*(n-5)*(n-6)*(n-4)*a(n-6)=0. - R. J. Mathar, Apr 22 2024
MAPLE
A371019 := proc(n)
add(9^k*binomial((n+1)/3, k)*binomial(n-1, k-1), k=0..n) ;
%/(n+1) ;
end proc:
seq(A371019(n), n=0..60) ; # R. J. Mathar, Apr 22 2024
PROG
(PARI) a(n) = sum(k=0, n, 9^k*binomial(n/3+1/3, k)*binomial(n-1, n-k))/(n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 15 2024
STATUS
approved