A359855 Array read by antidiagonals: T(n,k) is the number of Hamiltonian cycles in the stacked prism graph P_n X C_k, n >= 1, k >= 2.

1, 1, 4, 1, 3, 4, 1, 6, 6, 4, 1, 5, 22, 12, 4, 1, 8, 30, 82, 24, 4, 1, 7, 86, 160, 306, 48, 4, 1, 10, 126, 776, 850, 1142, 96, 4, 1, 9, 318, 1484, 7010, 4520, 4262, 192, 4, 1, 12, 510, 6114, 18452, 63674, 24040, 15906, 384, 4, 1, 11, 1182, 12348, 126426, 229698, 578090, 127860, 59362, 768, 4

Offset

1,3

Comments

The case for P_n X C_2 is determined using a double edge for C_2.

Links

Table of n, a(n) for n=1..66.

Eric Weisstein's World of Mathematics, Hamiltonian Cycle.

Eric Weisstein's World of Mathematics, Stacked Prism Graph.

Example

Array begins:
=========================================================
n\k | 2   3     4      5       6        7          8 ...
----+---------------------------------------------------
  1 | 1   1     1      1       1        1          1 ...
  2 | 4   3     6      5       8        7         10 ...
  3 | 4   6    22     30      86      126        318 ...
  4 | 4  12    82    160     776     1484       6114 ...
  5 | 4  24   306    850    7010    18452     126426 ...
  6 | 4  48  1142   4520   63674   229698    2588218 ...
  7 | 4  96  4262  24040  578090  2861964   53055038 ...
  8 | 4 192 15906 127860 5247824 35663964 1087362018 ...
   ...

Crossrefs

Columns 2..12 are A123932(n-1), A003945(n-1), A003699, A003731, A180582, A180583, A180584, A180585, A180586, A180587, A180588.

Rows 1..2 are A000012, A103889(n+1).

Cf. A222196 (order of recurrences), A222197 (main diagonal), A270273, A321172.

Sequence in context: A084118 A046071 A376353 * A078147 A376312 A362331

Adjacent sequences: A359852 A359853 A359854 * A359856 A359857 A359858

Keyword

nonn,tabl

Author

Andrew Howroyd, Feb 18 2025

Status

approved