Voozh

A026018

a(n) = number of (s(0), s(1), ..., s(2*n-1)) such that s(i) is a nonnegative integer and |s(i) - s(i-1)| = 1 for i = 1,2,...,n, s(0) = 2, s(2*n-1) = 7. Also a(n) = T(2*n-1,n-3), where T is the array defined in A026009.

1, 7, 36, 164, 702, 2898, 11696, 46512, 183141, 716243, 2788060, 10817820, 41880930, 161900910, 625272480, 2413491360, 9313307370, 35936613414, 138680365704, 535290282632, 2066802226236, 7983111461732, 30848211650592, 119257913003040, 461268870161645

(list; graph; refs; listen; history; text; internal format)

OFFSET

3,2

LINKS

Michael De Vlieger, Table of n, a(n) for n = 3..1667

Paul Drube, Raised k-Dyck paths, arXiv:2206.01194 [math.CO], 2022. See Appendix pp. 14-15.

FORMULA

Conjecture: -(n+5)*(3*n-37)*a(n) + 3*(-n^2-84*n-173)*a(n-1) + 2*(32*n^2+295*n+254)*a(n-2) - 8*(n+25)*(2*n-5)*a(n-3) = 0. - R. J. Mathar, Jun 20 2013

From Amiram Eldar, Oct 12 2025: (Start)

a(n) = binomial(2*n-1, n-3) - binomial(2*n-1, n-6).

a(n) ~ 3 * 4^(n+1) / (n^(3/2) * sqrt(Pi)). (End)

MATHEMATICA