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

0,2

Links

Table of n, a(n) for n=0..23.

Formula

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

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

Prog

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

Crossrefs

Sequence in context: A275794 A037746 A037627 * A037753 A037641 A361303

Adjacent sequences: A192366 A192367 A192368 * A192370 A192371 A192372

Keyword

nonn

Author

Eric Werley, Jun 29 2011

Extensions

Terms > 81123369 from Joerg Arndt, Jun 30 2011

Status

approved