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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 3 21:58 EST 2024. Contains 370518 sequences. (Running on oeis4.)