A355755 - OEIS

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

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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).