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Search: id:A054924
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| A054924 |
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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). |
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14
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| 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, 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, 0, 0, 0, 23, 89, 236, 486, 814, 1169, 1454, 1579, 1515, 1290, 970, 658, 400, 220, 114
(list; graph; listen)
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OFFSET
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1,11
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REFERENCES
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G. A. Baker et al., High-temperature expansions for the spin-1/2 Heisenberg model, Phys. Rev., 164 (1967), 800-817.
R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.
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.
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LINKS
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R. W. Robinson, Rows 1 to 20 of triangle, flattened
Gordon Royle, Small graphs
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EXAMPLE
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Triangle begins:
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;
0,0,0,0,0,6,13,19,22,20,14,9,5,2,1,1;
the last batch giving the numbers of connected graphs with 6 nodes and from 0 to 15 edges.
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MATHEMATICA
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A076263 gives a Mathematica program which produces the nonzero entries in each row.
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CROSSREFS
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Cf. A008406, A054925.
Other versions of this triangle: A046751, A076263, A054923, A046742.
Row sums give A001349, column sums give A002905. A046751 is essentially the same triangle. A054923 and A046742 give same triangle but read by columns.
Main diagonal is A000055. Next diagonal is A001429. Largest entry in each row gives A001437.
Sequence in context: A011265 A083747 A049334 this_sequence A025485 A046751 A124478
Adjacent sequences: A054921 A054922 A054923 this_sequence A054925 A054926 A054927
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KEYWORD
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nonn,easy,nice,tabf
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AUTHOR
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njas
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