A046742 Triangle of number of connected graphs with k >= 1 edges and n nodes (2 <= n <= k+1).

1, 0, 1, 0, 1, 2, 0, 0, 2, 3, 0, 0, 1, 5, 6, 0, 0, 1, 5, 13, 11, 0, 0, 0, 4, 19, 33, 23, 0, 0, 0, 2, 22, 67, 89, 47, 0, 0, 0, 1, 20, 107, 236, 240, 106, 0, 0, 0, 1, 14, 132, 486, 797, 657, 235, 0, 0, 0, 0, 9, 138, 814, 2075, 2678, 1806, 551, 0, 0, 0, 0, 5, 126, 1169, 4495, 8548, 8833, 5026, 1301

Offset

1,6

Links

Sean A. Irvine, Table of n, a(n) for n = 1..190

G. A. Baker et al., High-temperature expansions for the spin-1/2 Heisenberg model, Phys. Rev., 164 (1967), 800-817.

Gordon Royle, Small graphs

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. doi: 10.2172/4180737. Table 1 (complete up to 18 nodes)

Example

1;
0 1;
0 1 2;
0 0 2 3;
0 0 1 5 6;
0 0 1 5 13 11;
0 0 0 4 19 33 23;
0 0 0 2 22 67 89 47;
0 0 0 1 20 107 236 240 106;
0 0 0 1 14 132 486 797 657 235;
0 0 0 0 9 138 814 2075 2678 1806 551;
0 0 0 0 5 126 1169 4495 8548 8833 5026 1301;
0 0 0 0 2 95 1454 8404 22950 33851 28908 13999 3159;
0 0 0 0 1 64 1579 13855 53863 109844 130365 93569 39260 7741;
0 0 0 0 1 40 1515 20303 112618 313670 499888 489387 300748 110381 19320;
0 0 0 0 0 21 1290 26631 211866 803905 1694642 2179949 1799700 959374 311465 ...
... (so with 5 edges there's 1 graph with 4 nodes, 5 with 5 nodes and 1 with 6 nodes).

Crossrefs

Cf. A002905 (row sums), A008406, A046751, A054923, A054924 (transpose), A001349 (column sums).

Sequence in context: A296441 A091008 A111006 * A263138 A274637 A178516

Adjacent sequences: A046739 A046740 A046741 * A046743 A046744 A046745

Keyword

nonn,easy,nice,tabl

Author

N. J. A. Sloane

Extensions

Data corrected by Sean A. Irvine, Apr 23 2021

Status

approved