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%I #43 Apr 29 2022 17:15:32
%S 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 29,14,4,1,1,4,32,58,74,42,19,4,1,1,5,45,110,167,128,66,23,5,1
%N Triangle giving number of trees with n >= 3 nodes and diameter d >= 2.
%H 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 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 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 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 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 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F Reference gives recurrence.
%e 1
%e 1 1
%e 1 1 1
%e 1 2 2 1
%e 1 2 5 2 1
%e 1 3 8 7 3 1
%e 1 3 14 14 11 3 1
%e 1 4 21 32 29 14 4 1
%e 1 4 32 58 74 42 19 4 1
%e 1 5 45 110 167 128 66 23 5 1
%e 1 5 65 187 367 334 219 88 29 5 1
%e 1 6 88 322 755 850 645 328 123 34 6 1
%Y Cf. A000055 (row sums), A283826, A000094 (diameter 4), A000147 (diameter 5), A000251 (diameter 6), A000550 (diameter 7), A000306 (diameter 8).
%K nonn,tabl,easy,nice
%O 3,8
%A _N. J. A. Sloane_
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