

A268430


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


1



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
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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: A001428 A055726 A101500 * A047006 A127498 A149958
Adjacent sequences: A268427 A268428 A268429 * A268431 A268432 A268433


KEYWORD

nonn


AUTHOR

Ran Pan, Feb 04 2016


STATUS

approved



