%I #24 Dec 23 2017 05:09:12

%S 1,0,2,0,2,3,0,1,15,2,1,0,0,34,43,6,2,0,0,34,351,93,24,6,1,0,0,14,

%T 2167,1499,261,101,14,4,0,0,1,12301,22992,4400,1229,310,55,12,1,0,0,1,

%U 57628,338356,90870,17281,5145,948,220,36,4,0,0,0,185836,4692045,2013271,321788,84159,17894,3516,799,118,20,1

%N Irregular triangle read by rows: T(n,k) (n >= 2) is the number of cubic graphs on 2*n nodes with diameter k.

%C The number of terms in each row (the maximal diameter) begins 1,2,3,5,6,8,... . I don't know how this sequence continues.

%C The maximal diameter is now provided in A294732, taken from Gordon Royle's Cubic Graphs page. - _Hugo Pfoertner_, Dec 13 2017

%H Hugo Pfoertner, <a href="/A204329/b204329.txt">Table (flattened) of n, a(n) for n = 2..104</a> (rows 2..13).

%H F. C. Bussemaker, S. Cobeljic, L. M. Cvetkovic and J. J. Seidel, <a href="http://alexandria.tue.nl/repository/books/252909.pdf">Computer investigations of cubic graphs</a>, T.H.-Report 76-WSK-01, Technological University Eindhoven, Dept. Mathematics, 1976.

%H M. Meringer, <a href="https://sourceforge.net/projects/genreg/">GenReg</a>, Generation of regular graphs.

%H Gordon Royle, <a href="http://staffhome.ecm.uwa.edu.au/~00013890/remote/cubics/index.html">Cubic Graphs</a>, October 1996.

%e Triangle begins:

%e 1

%e 0 2

%e 0 2 3

%e 0 1 15 2 1

%e 0 0 34 43 6 2

%e 0 0 34 351 93 24 6 1

%e 0 0 14 2167 1499 261 101 14 4

%e 0 0 1 12301 22992 4400 1229 310 55 12 1

%e 0 0 1 57628 338356 90870 17281 5145 948 220 36 4

%e 0 0 0 185836 4692045 2013271 321788 84159 17894 3516 799 118 20 1

%e 0 0 0 341797 62398297 45891477 7325370 1558408 344829 63072 14082 2665 466 66 6

%e 0 0 0 298821 805690750 1059325766 187592813 32867106 7116021 1271737 253582 52710 9503 1779 245 30 1

%Y Cf. A002851, A294732.

%K nonn,tabf

%O 2,3

%A _N. J. A. Sloane_, Jan 14 2012

%E Extended using data from _Gordon Royle_'s Cubic Graphs page by _Hugo Pfoertner_, Dec 13 2017