login
A153335
Number of zig-zag paths from top to bottom of an n X n square whose color is not that of the top right corner.
5
0, 1, 2, 8, 18, 52, 116, 296, 650, 1556, 3372, 7768, 16660, 37416, 79592, 175568, 371034, 807604, 1697660, 3657464, 7654460, 16357496, 34106712, 72407728, 150499908, 317777032, 658707896, 1384524656, 2863150440, 5994736336
OFFSET
1,3
FORMULA
a(n) = (n+1)2^(n-2) - 2(n-1)binomial(n-2,(n-2)/2) for n even, a(n) = (n+1)2^(n-2) - (n)binomial(n-1,(n-1)/2) for n odd.
MATHEMATICA
Table[If[Mod[n, 2]==0, (n+1)*2^(n-2)-2(n-1) Binomial[n-2, (n-2)/2], (n+1)*2^(n-2)-(n) Binomial[n-1, (n-1)/2]], {n, 1, 30}] (* Indranil Ghosh, Feb 19 2017 *)
PROG
(Python)
import math
def C(n, r):
....f=math.factorial
....return f(n)/f(r)/f(n-r)
def A153335(n):
....if n%2==0: return str(int((n+1)*2**(n-2)-2*(n-1)*C(n-2, (n-2)/2)))
....else: return str(int((n+1)*2**(n-2)-(n)*C(n-1, (n-1)/2))) # Indranil Ghosh, Feb 19 2017
(PARI) a(n) = if (n % 2, (n+1)*2^(n-2) - n*binomial(n-1, (n-1)/2), (n+1)*2^(n-2) - 2*(n-1)*binomial(n-2, (n-2)/2)); \\ Michel Marcus, Feb 19 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Joseph Myers, Dec 24 2008
STATUS
approved