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 A034853 Triangle giving number of trees with n >= 3 nodes and diameter d>=2. 8
 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, 29, 14, 4, 1, 1, 4, 32, 58, 74, 42, 19, 4, 1, 1, 5, 45, 110, 167, 128, 66, 23, 5, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 3,8 LINKS R. J. Mathar, Table of n, a(n) for n = 3..212 B. D. McKay, Lists of Trees sorted by diameter and Homeomorphically irreducible trees, with <= 22 nodes. [Cached copy of top page only, pdf file, no active links, with permission] J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478. J. Riordan, The enumeration of trees by height and diameter, IBM Journal 4 (1960), 473-478. (Annotated scanned copy) FORMULA Reference gives recurrence. EXAMPLE 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   29   14    4    1    1    4   32   58   74   42   19    4    1    1    5   45  110  167  128   66   23    5    1    1    5   65  187  367  334  219   88   29    5    1    1    6   88  322  755  850  645  328  123   34    6    1 CROSSREFS Cf. A000055 (row sums), A283826, A000094 (diameter 4), A000147 (diameter 5), A000251 (diameter 6), A000550 (diameter 7), A000306 (diameter 8). Sequence in context: A070166 A131373 A245185 * A242093 A244006 A110283 Adjacent sequences:  A034850 A034851 A034852 * A034854 A034855 A034856 KEYWORD nonn,tabl,easy,nice AUTHOR STATUS approved

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Last modified December 16 20:51 EST 2018. Contains 318189 sequences. (Running on oeis4.)