A298445 - OEIS

%I #30 Apr 28 2019 20:12:52

%S 1,2,4,11,33,1,142,12,1,1,822,162,39,16,1,2,1,0,0,1,6966,3183,1291,

%T 559,172,82,48,12,15,8,4,1,3,0,0,1,0,0,0,1,79853

%N Triangle T(n,k) read by rows: number of n-node simple graphs with rectilinear crossing number k (k=0..A014540(n)).

%C Computed up to n=8 using data provided by Geoffrey Exoo. (There appear to be some problems with n=9 data.)

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RectilinearCrossingNumber.html">Rectilinear Crossing Number</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SimpleGraph.html">Simple Graph</a>

%F T(n,0) = A005470(n).

%F T(n,1) = A307071(n).

%F kmax(n) = A014540(n).

%F T(n,kmax(n)) = 1 for n > 4.

%F Sum_{k=0..kmax(n)} T(n,k) = A000088(n).

%e Triangle begins:

%e 1

%e 2

%e 4

%e 11

%e 33, 1

%e 142, 12, 1, 1

%e 822, 162, 39, 16, 1, 2, 1, 0, 0, 1

%e 6966, 3183, 1291, 559, 172, 82, 48, 12, 15, 8, 4, 1, 3, 0, 0, 1, 0, 0, 0, 1

%Y Cf. A014540 (rectilinear crossing number for K_n).

%Y Cf. A298446 (counts for simple connected graphs).

%Y Cf. A307071 (number of simple graphs with crossing number 1).

%K nonn,tabf

%O 1,2

%A _Eric W. Weisstein_, Jan 19 2018

%E Corrected by _Eric W. Weisstein_, Mar 28 2019