A367047 G.f. satisfies A(x) = 1 - x^3 + x*A(x)^4.

1, 1, 4, 21, 136, 941, 6864, 52006, 405312, 3228654, 26170764, 215166638, 1789998808, 15040070843, 127450104568, 1087988783356, 9347556057040, 80766068931498, 701359680126592, 6117887649100980, 53581405635501276, 470988258063461393

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(3*(n-3*k)+1,k) * binomial(4*(n-3*k),n-3*k)/(3*(n-3*k)+1).

Prog

(PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(3*(n-3*k)+1, k)*binomial(4*(n-3*k), n-3*k)/(3*(n-3*k)+1));

Crossrefs

Cf. A226022, A367046.

Cf. A367043.

Sequence in context: A001909 A205077 A292928 * A209881 A288869 A052852

Adjacent sequences: A367044 A367045 A367046 * A367048 A367049 A367050

Keyword

nonn

Author

Seiichi Manyama, Nov 03 2023

Status

approved