A369280 Triangle read by rows: T(n,k) is the number of simple connected graphs on n unlabeled nodes with cooling number k = 1..(1+floor(n/2)).

1, 0, 1, 0, 2, 0, 3, 3, 0, 3, 18, 0, 4, 97, 11, 0, 4, 655, 194, 0, 5, 7599, 3469, 44, 0, 5, 169013, 90529, 1533, 0, 6, 7554994, 4108406, 52986, 179

Offset

1,5

Links

Table of n, a(n) for n=1..35.

Eric Weisstein's World of Mathematics, Connected Graph.

Eric Weisstein's World of Mathematics, Cooling Number.

Example

Triangle begins:
  1;
  0, 1;
  0, 2;
  0, 3,       3;
  0, 3,      18;
  0, 4,      97,      11;
  0, 4,     655,     194;
  0, 5,    7599,    3469,   44;
  0, 5,  169013,   90529,  1533;
  0, 6, 7554994, 4108406, 52986, 179;
  ...

Crossrefs

Row sums are A001349.

Cf. A369279 (counts for all simple graphs), A369278 (cooling number).

Sequence in context: A004557 A088276 A099838 * A127449 A328911 A138057

Adjacent sequences: A369277 A369278 A369279 * A369281 A369282 A369283

Keyword

nonn,tabf,more

Author

Eric W. Weisstein, Jan 18 2024

Status

approved