A384849 Triangle read by rows: T(n,k) is the number of simple graphs on n unlabeled nodes with degeneracy k, 0 <= k < n.

1, 1, 1, 1, 2, 1, 1, 5, 4, 1, 1, 9, 18, 5, 1, 1, 19, 85, 43, 7, 1, 1, 36, 471, 442, 85, 8, 1, 1, 75, 3378, 6979, 1758, 144, 10, 1, 1, 152, 31782, 166258, 70811, 5421, 231, 11, 1, 1, 328, 385205, 5892753, 5164116, 547170, 15239, 342, 13, 1

Offset

1,5

Links

Table of n, a(n) for n=1..55.

Eric Weisstein's World of Mathematics, Graph Degeneracy.

Wikipedia, Degeneracy (graph theory).

Formula

T(n,0) = T(n,n-1) = 1.

T(n,1) = A005195(n) - 1.

Example

Triangle begins:
  1;
  1,   1;
  1,   2,      1;
  1,   5,      4,       1;
  1,   9,     18,       5,       1;
  1,  19,     85,      43,       7,      1;
  1,  36,    471,     442,      85,      8,     1;
  1,  75,   3378,    6979,    1758,    144,    10,   1;
  1, 152,  31782,  166258,   70811,   5421,   231,  11,  1;
  1, 328, 385205, 5892753, 5164116, 547170, 15239, 342, 13, 1;
  ...

Crossrefs

Row sums are A000088.

Cf. A005195, A352067 (connected case).

Sequence in context: A263324 A284949 A263294 * A241500 A152924 A220738

Adjacent sequences: A384846 A384847 A384848 * A384850 A384851 A384852

Keyword

nonn,tabl

Author

Andrew Howroyd, Jun 10 2025

Status

approved