A000251 Number of trees of diameter 6.

1, 3, 11, 29, 74, 167, 367, 755, 1515, 2931, 5551, 10263, 18677, 33409, 59024, 102984, 177915, 304458, 516939, 871180, 1458882, 2428548, 4021670, 6627515, 10874462, 17770474, 28932739, 46943967, 75925797, 122433291, 196879385, 315759282, 505168033, 806290796, 1284034606, 2040485004, 3235965074, 5121801962, 8091411114, 12759606939, 20085832527, 31565046053, 49523414558, 77575278933, 121329065354, 189475663960, 295465391518, 460087656595, 715436020515, 1110994054004

Offset: 7

Author

N. J. A. Sloane

Keywords

• nonn

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Christian Sievers, Table of n, a(n) for n = 7..9286
• J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.
• Index entries for sequences related to trees

Crossrefs

Cf. A034853, A000550 (diameter 7).

Programs

PARI

\\ sh_euler is shifted Euler transform.
sh_euler(p)={my(m=serprec(p,x)-1); x*exp(sum(i=1, m, subst(p+O(x^(1+m\i)), x, x^i)/i))}
lista(n)={my(s0=x + O(x*x^n), s1=sh_euler(s0), s2=sh_euler(s1), s3=sh_euler(s2), r2=s2-s1, r3=s3-s2, t6=r3-r2*s2); Vec(t6)} \\ Christian Sievers, May 18 2023

Extensions

More terms from Sean A. Irvine, Nov 21 2010