%I A101204
%S A101204 1,0,1,1,0,1,1,1,2,1,3,4,5,4,1,9,16,22,16,7,1,32,75,112,86,41,10,1,133
%N A101204 Triangle read by rows: T(n,k) = number of planar trivalent (or cubic) 
               multigraphs with 2n nodes and exactly k double bonds, for 0 <= k 
               <= n.
%C A101204 The entries in the first two rows are "by convention".
%D A101204 A. T. Balaban, Enumeration of Cyclic Graphs, pp. 63-105 of A. T. Balaban, 
               ed., Chemical Applications of Graph Theory, Ac. Press, 1976; see 
               p. 92.
%e A101204 Triangle begins
%e A101204 1
%e A101204 0 1
%e A101204 1 0 1
%e A101204 1 1 2 1
%e A101204 3 4 5 4 1
%e A101204 9 16 22 16 7 1
%e A101204 32 75 112 86 41 10 1
%e A101204 133 ...
%Y A101204 Row sums give A005966. First column is A005964 (trivalent connected planar 
               graphs with 2n nodes). Second and third columns give A101205, A101206.
%Y A101204 Sequence in context: A088267 A117407 A082470 this_sequence A035043 A155963 
               A058684
%Y A101204 Adjacent sequences: A101201 A101202 A101203 this_sequence A101205 A101206 
               A101207
%K A101204 nonn,tabl
%O A101204 0,9
%A A101204 N. J. A. Sloane (njas(AT)research.att.com), Dec 13 2004