OFFSET
1,3
COMMENTS
Number of distinct asymmetric staircase walks connecting opposite corners of a square grid of side n > 1. - Christian Barrientos, Nov 25 2018
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
EXAMPLE
U = up, R = right Example of asymmetric staircase walk: URURUURR. - Christian Barrientos, Nov 29 2018
MATHEMATICA
Table[Binomial[2n, n]/2-(2^(n-1)+Mod[n+1, 2]Binomial[n-1, n/2-1]), {n, 30}]/2
PROG
(PARI) a(n) = (binomial(2*n, n)/2 - (2^(n-1) + if (((n+1) % 2), binomial( n-1, n/2-1))))/2; \\ Michel Marcus, Nov 25 2018
(Magma) [(Binomial(2*n, n) -(2^n +(1+(-1)^n)*Binomial(n-1, Floor(n/2)-1) ))/4: n in [1..30]]; // G. C. Greubel, Feb 17 2019
(Sage) [(binomial(2*n, n) -(2^n + (1+(-1)^n)*binomial(n-1, floor(n/2)-1)))/4 for n in (1..30)] # G. C. Greubel, Feb 17 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved