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%I #28 Apr 11 2021 06:39:58
%S 1,1,1,1,2,1,1,4,4,1,1,8,12,8,1,1,16,38,38,16,1,1,32,125,184,125,32,1,
%T 1,64,414,976,976,414,64,1,1,128,1369,5382,8512,5382,1369,128,1,1,256,
%U 4522,29739,79384,79384,29739,4522,256,1,1,512,14934,163496,752061,1262816,752061,163496,14934,512,1
%N Square array read by antidiagonals of self-avoiding rook paths joining opposite corners of n X k board.
%D S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 331-339.
%H Andrew Howroyd, <a href="/A064298/b064298.txt">Table of n, a(n) for n = 1..378</a>
%H Steven R. Finch, <a href="/FinchGammel.html">Self-Avoiding Walks of a Rook on a Chessboard</a> [From Steven Finch, Apr 20 2019]
%H Steven R. Finch, <a href="/FinchFlajolet.html">Self-Avoiding Walks of a Rook</a> [From Steven Finch, Apr 20 2019; mentioned in Finch's "Gammel" link above]
%H Steven R. Finch, <a href="/FinchMarxen.html">Table of Non-Overlapping Rook Paths</a> [From Steven Finch, Apr 20 2019; mentioned in Finch's "Gammel" link above]
%e The start of the sequence as table:
%e * 1 1 1 1 1 1 1 ...
%e * 1 2 4 8 16 32 64 ...
%e * 1 4 12 38 125 414 1369 ...
%e * 1 8 38 184 976 5382 29739 ...
%e * 1 16 125 976 8512 79384 752061 ...
%e * 1 32 414 5382 79384 1262816 20562673 ...
%e * 1 64 1369 29739 752061 20562673 575780564 ...
%o (Python)
%o # Using graphillion
%o from graphillion import GraphSet
%o import graphillion.tutorial as tl
%o def A064298(n, k):
%o if n == 1 or k == 1: return 1
%o universe = tl.grid(n - 1, k - 1)
%o GraphSet.set_universe(universe)
%o start, goal = 1, k * n
%o paths = GraphSet.paths(start, goal)
%o return paths.len()
%o print([A064298(j + 1, i - j + 1) for i in range(11) for j in range(i + 1)]) # _Seiichi Manyama_, Apr 06 2020
%Y A064297 together with its transpose.
%Y Rows and columns include A000012, A000079, A006192, A007786, A007787, A145403, A333812.
%Y Main diagonal is A007764.
%Y Cf. A271465.
%K nonn,tabl,walk
%O 1,5
%A _Henry Bottomley_, Sep 05 2001
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