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A034853 Triangle giving number of trees with n >= 3 nodes and diameter d >= 2.

%I A034853 #43 Apr 29 2022 17:15:32
%S A034853 1,1,1,1,1,1,1,2,2,1,1,2,5,2,1,1,3,8,7,3,1,1,3,14,14,11,3,1,1,4,21,32,
%T A034853 29,14,4,1,1,4,32,58,74,42,19,4,1,1,5,45,110,167,128,66,23,5,1
%N A034853 Triangle giving number of trees with n >= 3 nodes and diameter d >= 2.
%H A034853 R. J. Mathar, <a href="/A034853/b034853.txt">Table of n, a(n) for n = 3..212</a> (a(192) corrected by _Sean A. Irvine_, Apr 28 2022)
%H A034853 B. D. McKay, <a href="http://users.cecs.anu.edu.au/~bdm/data/trees.html">Lists of Trees sorted by diameter and Homeomorphically irreducible trees, with <= 22 nodes.</a>
%H A034853 B. D. McKay, <a href="/A000014/a000014.pdf">Lists of Trees sorted by diameter and Homeomorphically irreducible trees, with <= 22 nodes.</a> [Cached copy of top page only, pdf file, no active links, with permission]
%H A034853 J. Riordan, <a href="http://dx.doi.org/10.1147/rd.45.0473">Enumeration of trees by height and diameter</a>, IBM J. Res. Dev. 4 (1960), 473-478.
%H A034853 J. Riordan, <a href="/A007401/a007401_8.pdf">The enumeration of trees by height and diameter</a>, IBM Journal 4 (1960), 473-478. (Annotated scanned copy)
%H A034853 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F A034853 Reference gives recurrence.
%e A034853    1
%e A034853    1    1
%e A034853    1    1    1
%e A034853    1    2    2    1
%e A034853    1    2    5    2    1
%e A034853    1    3    8    7    3    1
%e A034853    1    3   14   14   11    3    1
%e A034853    1    4   21   32   29   14    4    1
%e A034853    1    4   32   58   74   42   19    4    1
%e A034853    1    5   45  110  167  128   66   23    5    1
%e A034853    1    5   65  187  367  334  219   88   29    5    1
%e A034853    1    6   88  322  755  850  645  328  123   34    6    1
%Y A034853 Cf. A000055 (row sums), A283826, A000094 (diameter 4), A000147 (diameter 5), A000251 (diameter 6), A000550 (diameter 7), A000306 (diameter 8).
%K A034853 nonn,tabl,easy,nice
%O A034853 3,8
%A A034853 _N. J. A. Sloane_