A153337 Number of zig-zag paths from top to bottom of a 2n-1 by 2n-1 square whose color is that of the top right corner

1, 4, 24, 136, 720, 3624, 17584, 83024, 383904, 1746280, 7839216, 34812144, 153204064, 669108496, 2903267040, 12526343584, 53779871552, 229895033832, 978965187184, 4154438114480, 17575883030496, 74150192517808

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

Example

a(3) = 3 * 2 ^ (2*3 - 2) - 2* (3 - 1) * binomial(2*3 - 2, 3 - 1) = 24. - Indranil Ghosh, Feb 19 2017

Mathematica

Table[(n)2^(2n-2)-2(n-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 A153337(n):
....return str(n*2**(2*n-2)-2*(n-1)*C(2*n-2, n-1)) # Indranil Ghosh, Feb 19 2017
(PARI) a(n) = n*2^(2*n-2) - 2*(n-1)*binomial(2*n-2, n-1); \\ Michel Marcus, Feb 19 2017

Crossrefs

Cf. A102699, A153334, A153335, A153336, A153338.

Sequence in context: A048180 A057391 A071079 * A122690 A183512 A364277

Adjacent sequences: A153334 A153335 A153336 * A153338 A153339 A153340

Keyword

easy,nonn

Author

Joseph Myers, Dec 24 2008

Status

approved