A349818 Central column (ignoring the zeros) of A349815, or leading entries in rows of A349816.

1, 1, 1, 2, 8, 13, 74, 124, 784, 1364, 9069, 16194, 111144, 202070, 1418196, 2612376, 18642208, 34682348, 250706548, 470066728, 3433030048, 6477333149, 47703926354, 90472092748, 670963514192, 1278016171132, 9534032792470, 18226719157820, 136658371126320

Offset: 0

Author

N. J. A. Sloane, Dec 24 2021

Keywords

• nonn

Comments

Note that the analogous sequence for A349812 is the Motzkin numbers A001006.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A001006, A349812, A349815, A349816.

Programs

PARI

a(n) = if(n==0, 1, polcoef((-1 - x + x^2 + x^3)*(1 + x + x^2 + x^3)^(n-1), 3*n\2+1)) \\ Andrew Howroyd, Feb 28 2023

Formula

a(n) = [x^floor(3*n/2+1)](-1 - x + x^2 + 3*x^3)*(1 + x + x^2 + x^3)^(n-1) for n > 0. - Andrew Howroyd, Feb 28 2023

Extensions

Offset corrected and terms a(21) and beyond from Andrew Howroyd, Feb 28 2023