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A153336 Number of zig-zag paths from top to bottom of a 2n by 2n square whose color is that of the top right corner 5
1, 8, 52, 296, 1556, 7768, 37416, 175568, 807604, 3657464, 16357496, 72407728, 317777032, 1384524656, 5994736336, 25816193952, 110652549620, 472302724408, 2008499580504, 8513063608304, 35975584631128, 151621915797840 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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) = (2n+1)2^(2n-2) - 2(2n-1)binomial(2n-2,n-1).

EXAMPLE

a(3) = (2*3 + 1)*2 ^ (2*3 - 2) - 2*(2*3 - 1) * binomial(2*3 - 2, 3 - 1) = 52. - Indranil Ghosh, Feb 19 2017

MATHEMATICA

Table[(2n+1) 2^(2n-2)-2(2n-1) Binomial[2n-2, n-1], {n, 1, 22}] (* 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 A153336(n):

....return str((2*n+1)*2**(2*n-2)-2*(2*n-1)*C(2*n-2, n-1)) # Indranil Ghosh, Feb 19 2017

(PARI) a(n) = (2*n+1)*2^(2*n-2) - 2*(2*n-1)*binomial(2*n-2, n-1); \\ Michel Marcus, Feb 19 2017

CROSSREFS

Cf. A102699, A153334, A153335, A153337, A153338.

Sequence in context: A256047 A227732 A000432 * A080279 A279283 A257285

Adjacent sequences:  A153333 A153334 A153335 * A153337 A153338 A153339

KEYWORD

easy,nonn

AUTHOR

Joseph Myers, Dec 24 2008, Dec 31 2008

STATUS

approved

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Last modified September 21 22:17 EDT 2019. Contains 327284 sequences. (Running on oeis4.)