A355754 Irregular triangle read by rows: T(n,k) is the number of unlabeled n-node graphs with intersection number (or edge clique cover number) k; n >= 1, 0 <= k <= floor(n^2/4).

1, 1, 1, 1, 2, 1, 1, 3, 4, 2, 1, 1, 4, 9, 10, 7, 2, 1, 1, 5, 17, 36, 46, 30, 14, 4, 2, 1, 1, 6, 28, 97, 219, 281, 226, 116, 45, 18, 5, 1, 1, 1, 7, 43, 226, 872, 2104, 3170, 2927, 1774, 793, 290, 87, 37, 9, 3, 2, 1, 1, 8, 62, 472, 2966, 12882, 36595, 63842, 69294, 48881, 24939, 9808, 3387, 1059, 313, 107, 37, 9, 4, 1, 1

Offset

1,5

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) = 1.

T(n,1) = n-1.

T(n,2) = floor((n-2)*(2*n^2+7*n-12)/24) = A005744(n-2) = (4*n^3+6*n^2-52*n+45+3*(-1)^n)/48.

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  | 1  1
   3  | 1  2  1
   4  | 1  3  4   2   1
   5  | 1  4  9  10   7    2    1
   6  | 1  5 17  36  46   30   14    4    2   1
   7  | 1  6 28  97 219  281  226  116   45  18   5  1  1
   8  | 1  7 43 226 872 2104 3170 2927 1774 793 290 87 37  9  3  2  1

Crossrefs

Cf. A000088 (row sums), A355755.

Sequence in context: A331598 A123974 A238350 * A319844 A193736 A292975

Adjacent sequences: A355751 A355752 A355753 * A355755 A355756 A355757

Keyword

nonn,tabf

Author

Pontus von Brömssen, Jul 16 2022

Status

approved