A268430 Number of North-East paths from (0,0) to (n,n) that have even number of times bounce off y = x to the right.

1, 2, 5, 16, 53, 184, 654, 2368, 8689, 32216, 120434, 453248, 1715266, 6521584, 24894364, 95353472, 366324729, 1411015064, 5447548682, 21074836864, 81682204614, 317110750672, 1232951721604, 4800353915264, 18712880651802, 73030245143792, 285311648317172

Offset

0,2

Comments

This sequence is related to paired pattern P_2 in Section 3.2 in Pan and Remmel's link.

Links

Table of n, a(n) for n=0..26.

Ran Pan, Jeffrey B. Remmel, Paired patterns in lattice paths, arXiv:1601.07988 [math.CO], 2016.

Formula

G.f.: (-1 + 3*f(x) - 2*x*(-2 + 5*f(x)+ 6*f(x)*x))/(2*(4*x - 1) (-1 + 4*x*(1 + x))), where f(x) = sqrt(1 - 4*x).

a(n) = binomial(2*n,n) - A268431(n).

Crossrefs

Cf. A268407, A268429

Sequence in context: A101500 A339828 A047063 * A047006 A127498 A149958

Adjacent sequences: A268427 A268428 A268429 * A268431 A268432 A268433

Keyword

nonn

Author

Ran Pan, Feb 04 2016

Status

approved