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

0,4

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

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

Prog

(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

Crossrefs

Cf. A001006, A349812, A349815, A349816.

Sequence in context: A077241 A228469 A066567 * A329453 A319964 A357401

Adjacent sequences: A349815 A349816 A349817 * A349819 A349820 A349821

Keyword

nonn

Author

N. J. A. Sloane, Dec 24 2021

Extensions

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

Status

approved