%I A054924
%S A054924 1,0,1,0,0,1,1,0,0,0,2,2,1,1,0,0,0,0,3,5,5,4,2,1,1,0,0,0,0,0,6,13,19,22,
               20,14,9,5,
%T A054924 2,1,1,0,0,0,0,0,0,11,33,67,107,132,138,126,95,64,40,21,10,5,2,1,1,0,0,
               0,0,
%U A054924 0,0,0,23,89,236,486,814,1169,1454,1579,1515,1290,970,658,400,220,114
%N A054924 Triangle read by rows: T(n,k) = number of nonisomorphic unlabeled connected 
               graphs with n nodes and k edges (n >= 1, 0 <= k <= n(n-1)/2).
%D A054924 G. A. Baker et al., High-temperature expansions for the spin-1/2 Heisenberg 
               model, Phys. Rev., 164 (1967), 800-817.
%D A054924 R. W. Robinson, Numerical implementation of graph counting algorithms, 
               AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.
%D A054924 M. L. Stein and P. R. Stein, Enumeration of Linear Graphs and Connected 
               Linear Graphs up to p = 18 Points. Report LA-3775, Los Alamos Scientific 
               Laboratory of the University of California, Los Alamos, NM, Oct 1967.
%H A054924 R. W. Robinson, <a href="b054924.txt">Rows 1 to 20 of triangle, flattened</
               a>
%H A054924 Gordon Royle, <a href="http://www.cs.uwa.edu.au/~gordon/remote/graphs/
               index.html#nums">Small graphs</a>
%e A054924 Triangle begins:
%e A054924 1;
%e A054924 0,1;
%e A054924 0,0,1,1;
%e A054924 0,0,0,2,2,1,1;
%e A054924 0,0,0,0,3,5,5,4,2,1,1;
%e A054924 0,0,0,0,0,6,13,19,22,20,14,9,5,2,1,1;
%e A054924 the last batch giving the numbers of connected graphs with 6 nodes and 
               from 0 to 15 edges.
%t A054924 A076263 gives a Mathematica program which produces the nonzero entries 
               in each row.
%Y A054924 Cf. A008406, A054925.
%Y A054924 Other versions of this triangle: A046751, A076263, A054923, A046742.
%Y A054924 Row sums give A001349, column sums give A002905. A046751 is essentially 
               the same triangle. A054923 and A046742 give same triangle but read 
               by columns.
%Y A054924 Main diagonal is A000055. Next diagonal is A001429. Largest entry in 
               each row gives A001437.
%Y A054924 Sequence in context: A011265 A083747 A049334 this_sequence A025485 A046751 
               A124478
%Y A054924 Adjacent sequences: A054921 A054922 A054923 this_sequence A054925 A054926 
               A054927
%K A054924 nonn,easy,nice,tabf
%O A054924 1,11
%A A054924 N. J. A. Sloane (njas(AT)research.att.com).