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 A333580 Square array T(n,k), n >= 1, k >= 1, read by antidiagonals, where T(n,k) is the number of Hamiltonian paths in an n X k grid starting at the lower left corner and finishing in the upper right corner. 10
 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 2, 0, 1, 1, 1, 4, 4, 1, 1, 1, 0, 8, 0, 8, 0, 1, 1, 1, 16, 20, 20, 16, 1, 1, 1, 0, 32, 0, 104, 0, 32, 0, 1, 1, 1, 64, 111, 378, 378, 111, 64, 1, 1, 1, 0, 128, 0, 1670, 0, 1670, 0, 128, 0, 1, 1, 1, 256, 624, 6706, 10204, 10204, 6706, 624, 256, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,13 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..378 FORMULA T(n,k) = T(k,n). EXAMPLE Square array T(n,k) begins: 1, 1, 1, 1, 1, 1, 1, 1, ... 1, 0, 1, 0, 1, 0, 1, 0, ... 1, 1, 2, 4, 8, 16, 32, 64, ... 1, 0, 4, 0, 20, 0, 111, 0, ... 1, 1, 8, 20, 104, 378, 1670, 6706, ... 1, 0, 16, 0, 378, 0, 10204, 0, ... 1, 1, 32, 111, 1670, 10204, 111712, 851073, ... 1, 0, 64, 0, 6706, 0, 851073, 0, ... PROG (Python) # Using graphillion from graphillion import GraphSet import graphillion.tutorial as tl def A333580(n, k): if n == 1 or k == 1: return 1 universe = tl.grid(n - 1, k - 1) GraphSet.set_universe(universe) start, goal = 1, k * n paths = GraphSet.paths(start, goal, is_hamilton=True) return paths.len() print([A333580(j + 1, i - j + 1) for i in range(12) for j in range(i + 1)]) CROSSREFS Rows n=1..10 (with 0 omitted) give: A000012, A000035, A011782(n-1), A014523, A014584, A333581, A333582, A333583, A333584, A333585. T(2*n-1,2*n-1) gives A001184(n-1). Cf. A271592. Sequence in context: A134655 A262124 A199954 * A219987 A077614 A336396 Adjacent sequences: A333577 A333578 A333579 * A333581 A333582 A333583 KEYWORD nonn,tabl AUTHOR Seiichi Manyama, Mar 27 2020 STATUS approved

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Last modified December 9 23:05 EST 2022. Contains 358710 sequences. (Running on oeis4.)