This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A064298 #28 Apr 11 2021 06:39:58 %S A064298 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 A064298 1,64,414,976,976,414,64,1,1,128,1369,5382,8512,5382,1369,128,1,1,256, %U A064298 4522,29739,79384,79384,29739,4522,256,1,1,512,14934,163496,752061,1262816,752061,163496,14934,512,1 %N A064298 Square array read by antidiagonals of self-avoiding rook paths joining opposite corners of n X k board. %D A064298 S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 331-339. %H A064298 Andrew Howroyd, <a href="/A064298/b064298.txt">Table of n, a(n) for n = 1..378</a> %H A064298 Steven R. Finch, <a href="/FinchGammel.html">Self-Avoiding Walks of a Rook on a Chessboard</a> [From Steven Finch, Apr 20 2019] %H A064298 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 A064298 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 A064298 The start of the sequence as table: %e A064298 * 1 1 1 1 1 1 1 ... %e A064298 * 1 2 4 8 16 32 64 ... %e A064298 * 1 4 12 38 125 414 1369 ... %e A064298 * 1 8 38 184 976 5382 29739 ... %e A064298 * 1 16 125 976 8512 79384 752061 ... %e A064298 * 1 32 414 5382 79384 1262816 20562673 ... %e A064298 * 1 64 1369 29739 752061 20562673 575780564 ... %o A064298 (Python) %o A064298 # Using graphillion %o A064298 from graphillion import GraphSet %o A064298 import graphillion.tutorial as tl %o A064298 def A064298(n, k): %o A064298 if n == 1 or k == 1: return 1 %o A064298 universe = tl.grid(n - 1, k - 1) %o A064298 GraphSet.set_universe(universe) %o A064298 start, goal = 1, k * n %o A064298 paths = GraphSet.paths(start, goal) %o A064298 return paths.len() %o A064298 print([A064298(j + 1, i - j + 1) for i in range(11) for j in range(i + 1)]) # _Seiichi Manyama_, Apr 06 2020 %Y A064298 A064297 together with its transpose. %Y A064298 Rows and columns include A000012, A000079, A006192, A007786, A007787, A145403, A333812. %Y A064298 Main diagonal is A007764. %Y A064298 Cf. A271465. %K A064298 nonn,tabl,walk %O A064298 1,5 %A A064298 _Henry Bottomley_, Sep 05 2001