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

1, 8, 52, 296, 1556, 7768, 37416, 175568, 807604, 3657464, 16357496, 72407728, 317777032, 1384524656, 5994736336, 25816193952, 110652549620, 472302724408, 2008499580504, 8513063608304, 35975584631128, 151621915797840

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