A153334 Number of zig-zag paths from top to bottom of an n X n square whose color is that of the top right corner.

1, 1, 4, 8, 24, 52, 136, 296, 720, 1556, 3624, 7768, 17584, 37416, 83024, 175568, 383904, 807604, 1746280, 3657464, 7839216, 16357496, 34812144, 72407728, 153204064, 317777032, 669108496, 1384524656, 2903267040, 5994736336

Offset

1,3

Links

Indranil Ghosh, Table of n, a(n) for n = 1..1000

Joseph Myers, BMO 2008--2009 Round 1 Problem 1---Generalisation

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-1)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-1)  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 A153334(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-1)*C(n-1, (n-1)/2))) # Indranil Ghosh, Feb 19 2017

Crossrefs

Cf. A102699, A153335, A153336, A153337, A153338.

Sequence in context: A208901 A319721 A115641 * A332871 A116719 A159612

Adjacent sequences: A153331 A153332 A153333 * A153335 A153336 A153337

Keyword

easy,nonn

Author

Joseph Myers, Dec 24 2008

Status

approved