A090224 Number of possible positions for n discs on a standard 7 X 6 board of Connect-Four.

1, 7, 56, 252, 1260, 4620, 18480, 59815, 206780, 605934, 1869840, 5038572, 14164920, 35459424, 91871208, 214864650, 516936420, 1134183050, 2546423880, 5252058812, 11031780760, 21406686756, 42121344720, 76871042612, 141627466344, 242619996500, 417750499600

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..42 (copied from the Victor Allis link)

Victor Allis, A Knowledge-Based Approach of Connect-Four--The Game Is Solved: White Wins.

John Tromp, John's Connect Four Playground, viewed Jan 23 2014.

Eric Weisstein's World of Mathematics, Connect-Four

Wikipedia, Connect Four

Example

a(2) = 2 * binomial(8,2) since there are binomial(8,2) ways to distribute 2 discs over 7 columns and 2 ways to color them black and white. - John Tromp, May 24 2012

Crossrefs

Cf. A212693 (legal positions after n plies).

Sequence in context: A044526 A153797 A244727 * A237647 A047664 A055345

Adjacent sequences: A090221 A090222 A090223 * A090225 A090226 A090227

Keyword

nonn,fini,full,nice

Author

Eric W. Weisstein, Nov 24 2003

Status

approved