Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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