%I #13 Mar 11 2023 19:48:36

%S 1,0,0,0,1,1,1,1,1,2,2,5,5,5,2,2,6,11,33,48,66,48,33,11,6,21,68,257,

%T 556,950,1071,950,556,257,68,21,94,510,2443,7126,15393,23644,27606,

%U 23644,15393,7126,2443,510,94,540,4712,27682,102122,270957,526783,781292,887305,781292,526783,270957,102122,27682,4712,540

%N Triangle read by rows: T(n,k) is the number of bicolored cubic graphs on 2n unlabeled vertices with k vertices of the first color, n >= 0, 0 <= k <= 2*n.

%C Adjacent vertices may have the same color.

%H Andrew Howroyd, <a href="/A361361/b361361.txt">Table of n, a(n) for n = 0..440</a> (rows 0..20)

%e Triangle begins:

%e 1

%e 0, 0, 0;

%e 1, 1, 1, 1, 1;

%e 2, 2, 5, 5, 5, 2, 2;

%e 6, 11, 33, 48, 66, 48, 33, 11, 6;

%e 21, 68, 257, 556, 950, 1071, 950, 556, 257, 68, 21;

%e ...

%Y Columns k=0..2 are A005638, A361410, A361411.

%Y Row sums are A361362.

%Y Central coefficients are A361409.

%Y Cf. A321304 (connected), A361404.

%K nonn,tabf

%O 0,10

%A _Andrew Howroyd_, Mar 10 2023