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

Author

Eric W. Weisstein, Nov 24 2003

Keywords

• nonn
• fini
• full
• nice

Examples

			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
		

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

Crossrefs

Cf. A212693 (legal positions after n plies).