A391033 Expansion of g/(1 - x^3*g^3), where g = 1+x*g^2 is the g.f. of A000108.

1, 1, 2, 6, 18, 56, 181, 601, 2037, 7019, 24515, 86593, 308799, 1110249, 4020162, 14647422, 53660766, 197545356, 730413708, 2711279418, 10099991244, 37745850414, 141480728682, 531739303520, 2003456606698, 7565853390028, 28632482460486, 108571883092112, 412452561980414

Offset

0,3

Links

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

Formula

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

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

Prog

(PARI) a(n) = sum(k=0, n\3, (3*k+1)*binomial(2*n-3*k+1, n-3*k)/(2*n-3*k+1));

Crossrefs

Cf. A078483, A279561, A390478, A391029, A391031.

Cf. A000108.

Sequence in context: A111961 A190861 A071721 * A125306 A352076 A378426

Adjacent sequences: A391030 A391031 A391032 * A391034 A391035 A391036

Keyword

nonn

Author

Seiichi Manyama, Nov 26 2025

Status

approved