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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. 5
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 (list; graph; refs; listen; history; text; internal format)
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 * A116719 A159612 A099176

Adjacent sequences:  A153331 A153332 A153333 * A153335 A153336 A153337

KEYWORD

easy,nonn

AUTHOR

Joseph Myers, Dec 24 2008

STATUS

approved

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Last modified September 21 23:55 EDT 2019. Contains 327286 sequences. (Running on oeis4.)