A355755 Irregular triangle read by rows: T(n,k) is the number of unlabeled connected n-node graphs with intersection number (or edge clique cover number) k; n >= 1, 0 <= k <= floor(n^2/4).

1, 0, 1, 0, 1, 1, 0, 1, 2, 2, 1, 0, 1, 4, 7, 6, 2, 1, 0, 1, 6, 22, 36, 27, 13, 4, 2, 1, 0, 1, 9, 53, 161, 242, 209, 111, 43, 17, 5, 1, 1, 0, 1, 12, 114, 611, 1766, 2903, 2793, 1723, 773, 284, 86, 36, 9, 3, 2, 1, 0, 1, 16, 221, 1987, 10517, 33078, 60639, 67379, 48035, 24628, 9715, 3349, 1049, 310, 105, 36, 9, 4, 1, 1

Offset

1,9

Links

Eric W. Weisstein, Table of n, a(n) for n = 1..108

Paul Erdős, A. W. Goodman, and Louis Pósa, The representation of a graph by set intersections, Canadian Journal of Mathematics 18 (1966), 106-112.

Eric Weisstein's World of Mathematics, Intersection Number

Wikipedia, Intersection number

Formula

T(n,0) = 0 if n > 1.

T(n,1) = 1.

T(n,2) = floor((n-1)^2/4) = A002620(n-1).

Example

Triangle begins:
  n\k | 0  1  2   3   4    5    6    7    8   9  10 11 12 13 14 15 16
  ----+--------------------------------------------------------------
   1  | 1
   2  | 0  1
   3  | 0  1  1
   4  | 0  1  2   2   1
   5  | 0  1  4   7   6    2    1
   6  | 0  1  6  22  36   27   13    4    2   1
   7  | 0  1  9  53 161  242  209  111   43  17   5  1  1
   8  | 0  1 12 114 611 1766 2903 2793 1723 773 284 86 36  9  3  2  1

Crossrefs

Cf. A001349 (row sums), A002620, A355754.

Sequence in context: A055290 A125629 A339160 * A141335 A133624 A377941

Adjacent sequences: A355752 A355753 A355754 * A355756 A355757 A355758

Keyword

nonn,tabf

Author

Pontus von Brömssen, Jul 16 2022

Status

approved