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%I #14 Dec 09 2022 16:05:13
%S 1,1,2,2,10,20,248,1072,31178,270026,18806964,329412610,54393195014,
%T 1931171930256,749416883107560,54217060622200086
%N Number of self-avoiding paths of length 2*(n+A002620(n-1)) along the edges of a grid with n X n square cells, which do not pass above the diagonal, start at the lower left corner and finish at the upper right corner.
%F a(n) = A340043(n, A002620(n-1)).
%e 3 X 3 square cells
%e *---*---*---E
%e | | | |
%e *---*---*---*
%e | | | |
%e *---*---*---*
%e | | | |
%e S---*---*---*
%e a(3) = 2;
%e E E
%e | |
%e * *---*
%e | |
%e *---* * *---*
%e | | | |
%e S---* *---* S---*---*---*
%Y Cf. A000108, A002620, A340005, A340043.
%K nonn,more
%O 0,3
%A _Seiichi Manyama_, Dec 09 2022