OFFSET
0,4
FORMULA
a(n) = Sum_{k=0..floor(n/2)} 9^k * binomial((n+k)/3-1,k).
D-finite with recurrence -(n-1)*(n-2)*(n-8)*a(n) +3*(9*n^3-123*n^2+490*n-616)*a(n-2) +(n-1)*(n-2)*(n-8)*a(n-3) +9*(-27*n^3+441*n^2-2318*n+3984)*a(n-4) +6*(-3*n^3+45*n^2-206*n+284)*a(n-5) +81*(3*n-20)*(n-6)*(3*n-19)*a(n-6) +9*(3*n-20)*(n-6)*(3*n-19)*a(n-7)=0. - R. J. Mathar, Jun 07 2024
a(n) == 1 (mod 3). - Seiichi Manyama, Jun 11 2024
MAPLE
A371456 := proc(n)
add(9^k*binomial((n+k)/3-1, k), k=0..floor(n/2)) ;
end proc:
seq(A371456(n), n=0..70) ; # R. J. Mathar, Jun 07 2024
PROG
(PARI) a(n) = sum(k=0, n\2, 9^k*binomial((n+k)/3-1, k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 07 2024
STATUS
approved