cp's OEIS Frontend

A212693 Number of legal 7 X 6 Connect-Four positions after n plies.

%I A212693 #56 Aug 28 2025 19:32:02
%S A212693 1,7,49,238,1120,4263,16422,54859,184275,558186,1662623,4568683,
%T A212693 12236101,30929111,75437595,176541259,394591391,858218743,1763883894,
%U A212693 3568259802,6746155945,12673345045,22010823988,38263228189,60830813459,97266114959,140728569039
%N A212693 Number of legal 7 X 6 Connect-Four positions after n plies.
%C A212693 Sum of all 43 terms is 4531985219092 as computed by Edelkamp and Kissmann (see link).
%H A212693 John Tromp, <a href="/A212693/b212693.txt">Table of n, a(n) for n = 0..42</a> (copied from the P. Kissmann link)
%H A212693 Dennis Aanstoot, <a href="https://essay.utwente.nl/92857/1/Aanstoot_MA_FMT.pdf">Graph rewriters as components</a>, Univ. of Twente (Netherlands, 2022).
%H A212693 S. Edelkamp and P. Kissmann, <a href="https://web.archive.org/web/20160323025034/http://www.tzi.de/~edelkamp/lectures/ae/slide/AE-SymbolischeSuche.pdf">Symbolic Classification of General Two-Player Games</a>
%H A212693 Brady Haran, <a href="http://www.youtube.com/watch?v=yDWPi1pZ0Po">Connect Four</a>, Numberphile video, 2013.
%H A212693 Johannes Niklas Hartmann, <a href="https://arxiv.org/abs/2105.12514">Finding optimal strategies in sequential games with the novel selection monad</a>, arXiv:2105.12514 [cs.AI], 2021.
%H A212693 P. Kissmann, <a href="http://www.tzi.de/~edelkamp/lectures/ae/slide/AE-SymbolischeSuche.pdf">Algorithm Engineering - Symbolische Suche</a> [broken link]
%H A212693 John Tromp, <a href="http://tromp.github.io/c4/c4.html">John's Connect Four Playground</a>
%H A212693 2swap, <a href="https://www.youtube.com/watch?v=i9pBeuBeupY">Beating connect 4 with graph theory</a>, YouTube video (2024).
%e A212693 a(3) = 7 * (1*7 + 6*(5/2 + 2)) = 238 because 3 discs played in different columns can be transposed in two ways.
%Y A212693 Cf. A090224 (upper bound), A013582.
%K A212693 nonn,fini,full,changed
%O A212693 0,2
%A A212693 _John Tromp_, May 23 2012