A392422 Array read by antidiagonals: T(n,k) is the number of Hamiltonian cycles in the n X k truncated square lattice graph.

3, 4, 4, 8, 24, 8, 16, 56, 56, 16, 32, 160, 378, 160, 32, 64, 352, 2644, 2644, 352, 64, 128, 896, 18478, 23736, 18478, 896, 128, 256, 1920, 130992, 376440, 376440, 130992, 1920, 256, 512, 4608, 931274, 3364312, 10582480, 3364312, 931274, 4608, 512, 1024, 9728, 6629564, 48690960, 255107524, 255107524, 48690960, 6629564, 9728, 1024

Offset

1,1

Links

Andrew Howroyd, Table of n, a(n) for n = 1..120 (first 15 antidiagonals)

Eric Weisstein's World of Mathematics, Hamiltonian Cycle.

Eric Weisstein's World of Mathematics, Truncated Square Lattice Graph.

Formula

T(n,k) = T(k,n).

T(n,1) = 2^n for n > 1.

Example

Array begins:
====================================================
n\k |  1   2      3       4         5          6 ...
----+-----------------------------------------------
  1 |  3   4      8      16        32         64 ...
  2 |  4  24     56     160       352        896 ...
  3 |  8  56    378    2644     18478     130992 ...
  4 | 16 160   2644   23736    376440    3364312 ...
  5 | 32 352  18478  376440  10582480  255107524 ...
  6 | 64 896 130992 3364312 255107524 7596623856 ...
  ...

Crossrefs

Main diagonal is A393482.

Cf. A270273.

Sequence in context: A292729 A328989 A339190 * A137529 A245258 A086180

Adjacent sequences: A392419 A392420 A392421 * A392423 A392424 A392425

Keyword

nonn,tabl

Author

Andrew Howroyd, Feb 17 2026

Status

approved