A192369 Number of lattice paths from (0,0) to (n,n) using steps (0,1), (0,2), (1,0), (2,0), and (2,2).

1, 2, 15, 90, 617, 4248, 29945, 213404, 1535661, 11129314, 81123369, 594092166, 4367701295, 32216566492, 238301617605, 1766979857196, 13129849298327, 97746629874786, 728897653778335, 5443488765350770, 40706993579981847, 304779612155116444, 2284440756129389775, 17139937071103287600

Offset: 0

Author

Eric Werley, Jun 29 2011

Keywords

• nonn

Comments

Diagonal of the rational function 1 / (1 - x - y - x^2 - y^2 - (x*y)^2). - Ilya Gutkovskiy, Apr 23 2025

Programs

Maple

p4 := (x-1)*(x^3+5*x^2+7*x-1);
ogf := sqrt(((2*x^2+4*x-3)/p4-2/sqrt(p4))/(4*x^2-8*x-5));
series(ogf, x=0, 30); # Mark van Hoeij, Apr 16 2013

PARI

/* same as in A092566 but use */
steps=[[0,1], [0,2], [1,0], [2,0], [2,2]];
/* Joerg Arndt, Jun 30 2011 */

Formula

G.f. is a nested square root, see Maple program. - Mark van Hoeij, Apr 16 2013

Extensions

Terms > 81123369 from Joerg Arndt, Jun 30 2011