A005334
Number of labeled nonseparable (or 2-connected) bicolored graphs with n nodes of the first color and n nodes of the second color.
Original entry on oeis.org
1, 1, 34, 7037, 6317926, 21073662977, 251973418941994, 10878710974408306717, 1727230695707098000548430, 1028983422758641650604161840065, 2342608062302306704492272616530549874, 20683716767972841770515007707311751484424893
Offset: 1
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
- Andrew Howroyd, Table of n, a(n) for n = 1..50
- F. Harary and R. W. Robinson, Labeled bipartite blocks, Canad. J. Math., 31 (1979), 60-68.
- F. Harary and R. W. Robinson, Labeled bipartite blocks, Canad. J. Math., 31 (1979), 60-68. (Annotated scanned copy)
Main diagonal of
A123301 as an array.
A123474
Triangle read by rows: T(n,k) = number of labeled bicolored nonseparable graphs with k points in one color class and n-k points in the other class. The classes are interchangeable if k = n-k. Here n >= 2, k=1..n-1.
Original entry on oeis.org
1, 0, 0, 0, 3, 0, 0, 10, 10, 0, 0, 15, 340, 15, 0, 0, 21, 6965, 6965, 21, 0, 0, 28, 51296, 246295, 51296, 28, 0, 0, 36, 326676, 14750946, 14750946, 326676, 36, 0, 0, 45, 1917840, 322476210, 796058676, 322476210, 1917840, 45, 0, 0, 55, 10683255
Offset: 2
Triangle begins:
1;
0, 0;
0, 3, 0;
0, 10, 10, 0;
0, 15, 340, 15, 0;
0, 21, 6965, 6965, 21, 0;
0, 28, 51296, 246295, 51296, 28, 0;
...
Formatted as an array:
==========================================================
m/n | 1 2 3 4 5 6
----+-----------------------------------------------------
1 | 1 0 0 0 0 0 ...
2 | 0 3 10 15 21 28 ...
3 | 0 10 340 6965 51296 326676 ...
4 | 0 15 6965 246295 14750946 322476210 ...
5 | 0 21 51296 14750946 796058676 105725374062 ...
6 | 0 28 326676 322476210 105725374062 9736032295374 ...
...
- R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1977.
A005336
Number of labeled nonseparable (or 2-connected) bipartite graphs with 2n nodes.
Original entry on oeis.org
1, 3, 355, 297619, 1120452771, 15350524923547, 738416821509929731, 126430202628042630866787, 78847417416749666369637926851, 183373380693566591129149674727445419, 1623847327688450079238401833083018045926051, 55669578575421273854874611540671620662810228887603
Offset: 1
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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