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 A332307 Array read by antidiagonals: T(m,n) is the number of (undirected) Hamiltonian paths in the m X n grid graph. 7
 1, 1, 1, 1, 4, 1, 1, 8, 8, 1, 1, 14, 20, 14, 1, 1, 22, 62, 62, 22, 1, 1, 32, 132, 276, 132, 32, 1, 1, 44, 336, 1006, 1006, 336, 44, 1, 1, 58, 688, 3610, 4324, 3610, 688, 58, 1, 1, 74, 1578, 12010, 26996, 26996, 12010, 1578, 74, 1, 1, 92, 3190, 38984, 109722, 229348, 109722, 38984, 3190, 92, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..435 J. L. Jacobsen, Exact enumeration of Hamiltonian circuits, walks and chains in two and three dimensions, J. Phys. A: Math. Theor. 40 (2007) 14667-14678. J.-M. Mayer, C. Guez and J. Dayantis, Exact computer enumeration of the number of Hamiltonian paths in small square plane lattices, Physical Review B, Vol. 42 Number 1, 1990. Eric Weisstein's World of Mathematics, Grid Graph Eric Weisstein's World of Mathematics, Hamiltonian Path FORMULA T(n,m) = T(m,n). EXAMPLE Array begins: ================================================ m\n | 1  2   3     4      5       6        7 ----+-------------------------------------------   1 | 1  1   1     1      1       1        1 ...   2 | 1  4   8    14     22      32       44 ...   3 | 1  8  20    62    132     336      688 ...   4 | 1 14  62   276   1006    3610    12010 ...   5 | 1 22 132  1006   4324   26996   109722 ...   6 | 1 32 336  3610  26996  229348  1620034 ...   7 | 1 44 688 12010 109722 1620034 13535280 ...   ... CROSSREFS Rows n=1..6 are A000012, A003682, A003685, A003695, A003778, A145402. Main diagonal is A120443. Cf. A064298, A231829, A271465, A271592, A288518, A321172. Sequence in context: A132789 A319251 A100754 * A296405 A174035 A303888 Adjacent sequences:  A332304 A332305 A332306 * A332308 A332309 A332310 KEYWORD nonn,tabl AUTHOR Andrew Howroyd, Feb 09 2020 STATUS approved

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Last modified April 23 07:37 EDT 2021. Contains 343201 sequences. (Running on oeis4.)