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
Examples
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
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.