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A212693
Number of legal 7 X 6 Connect-Four positions after n plies.
6
1, 7, 49, 238, 1120, 4263, 16422, 54859, 184275, 558186, 1662623, 4568683, 12236101, 30929111, 75437595, 176541259, 394591391, 858218743, 1763883894, 3568259802, 6746155945, 12673345045, 22010823988, 38263228189, 60830813459, 97266114959, 140728569039
OFFSET
0,2
COMMENTS
Sum of all 43 terms is 4531985219092 as computed by Edelkamp and Kissmann (see link).
LINKS
John Tromp, Table of n, a(n) for n = 0..42 (copied from the P. Kissmann link)
Dennis Aanstoot, Graph rewriters as components, Univ. of Twente (Netherlands, 2022).
Brady Haran, Connect Four, Numberphile video, 2013.
Johannes Niklas Hartmann, Finding optimal strategies in sequential games with the novel selection monad, arXiv:2105.12514 [cs.AI], 2021.
EXAMPLE
a(3) = 7 * (1*7 + 6*(5/2 + 2)) = 238 because 3 discs played in different columns can be transposed in two ways.
CROSSREFS
Cf. A090224 (upper bound), A013582.
Sequence in context: A141783 A181479 A223842 * A223615 A188768 A188757
KEYWORD
nonn,fini,full
AUTHOR
John Tromp, May 23 2012
STATUS
approved