A355755 - OEIS

%I #19 Apr 26 2024 07:58:17

%S 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,

%T 161,242,209,111,43,17,5,1,1,0,1,12,114,611,1766,2903,2793,1723,773,

%U 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

%N 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).

%H Eric W. Weisstein, <a href="/A355755/b355755.txt">Table of n, a(n) for n = 1..108</a>

%H Paul Erdős, A. W. Goodman, and Louis Pósa, <a href="https://doi.org/10.4153%2FCJM-1966-014-3">The representation of a graph by set intersections</a>, Canadian Journal of Mathematics 18 (1966), 106-112.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IntersectionNumber.html">Intersection Number</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Intersection_number_(graph_theory)">Intersection number</a>

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

%F T(n,1) = 1.

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

%e Triangle begins:

%e   n\k | 0  1  2   3   4    5    6    7    8   9  10 11 12 13 14 15 16

%e   ----+--------------------------------------------------------------

%e    1  | 1

%e    2  | 0  1

%e    3  | 0  1  1

%e    4  | 0  1  2   2   1

%e    5  | 0  1  4   7   6    2    1

%e    6  | 0  1  6  22  36   27   13    4    2   1

%e    7  | 0  1  9  53 161  242  209  111   43  17   5  1  1

%e    8  | 0  1 12 114 611 1766 2903 2793 1723 773 284 86 36  9  3  2  1

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

%K nonn,tabf

%O 1,9

%A _Pontus von Brömssen_, Jul 16 2022