cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A352210 Largest number of maximal 2-degenerate node-induced subgraphs of an n-node graph.

Original entry on oeis.org

1, 1, 1, 4, 10, 20, 35, 56, 97
Offset: 1

Views

Author

Pontus von Brömssen, Mar 08 2022

Keywords

Comments

This sequence is log-superadditive, i.e., a(m+n) >= a(m)*a(n). By Fekete's subadditive lemma, it follows that the limit of a(n)^(1/n) exists and equals the supremum of a(n)^(1/n).

Examples

			For 3 <= n <= 8, a(n) = binomial(n,3) = A000292(n-2) and the complete graph is optimal, but a(9) = 97 > binomial(9,3) with the optimal graph being the complement of the disjoint union of K_3 and K_{3,3}. The optimal graph is unique when 4 <= n <= 9.
		

Crossrefs

For a list of related sequences, see cross-references in A342211.

Formula

a(m+n) >= a(m)*a(n).
Limit_{n->oo} a(n)^(1/n) >= 97^(1/9) = 1.66246... .

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

Original entry on oeis.org

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

Views

Author

Andrew Howroyd, Jun 10 2025

Keywords

Examples

			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).

Formula

T(n,0) = T(n,n-1) = 1.
T(n,1) = A005195(n) - 1.
Showing 1-2 of 2 results.