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A090224
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Number of possible positions for n discs on a standard 7 X 6 board of Connect-Four.
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4
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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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
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EXAMPLE
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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
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CROSSREFS
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Cf. A212693 (legal positions after n plies).
Sequence in context: A044526 A153797 A244727 * A237647 A047664 A055345
Adjacent sequences: A090221 A090222 A090223 * A090225 A090226 A090227
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KEYWORD
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nonn,fini,full,nice
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AUTHOR
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Eric W. Weisstein, Nov 24 2003
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STATUS
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approved
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