A343168 Irregular triangle read by rows: T(n,k) (n>=1, 2 <= k <= n for n >= 2) gives number of graphs on n nodes that are isometrically embeddable into the Hamming graph H(n,k).

1, 1, 1, 1, 3, 1, 1, 4, 5, 1, 1, 12, 16, 5, 1, 1, 25, 61, 18, 5, 1, 1, 79, 239, 84, 18, 5, 1, 1, 212, 1053, 366, 86, 18, 5, 1, 1

Offset

1,5

Links

Table of n, a(n) for n=1..37.

Example

Triangle (with row sums) begins:
  n=1:    1                                                     1
  n=2:    1                                                     1
  n=3:    1     1                                               2
  n=4:    3     1     1                                         5
  n=5:    4     5     1     1                                  11
  n=6:   12    16     5     1     1                            35
  n=7:   25    61    18     5     1     1                     111
  n=8:   79   239    84    18     5     1     1               427

Crossrefs

See A343163-A343167 for the first three columns and their sums.

The row sums are A343162.

Sequence in context: A321876 A131238 A133380 * A105687 A209415 A058879

Adjacent sequences: A343165 A343166 A343167 * A343169 A343170 A343171

Keyword

nonn,more,tabf

Author

N. J. A. Sloane, Apr 19 2021, based on an email from Don Knuth

Status

approved