A000306 Number of trees of diameter 8.

1, 4, 19, 66, 219, 645, 1813, 4802, 12265, 30198, 72396, 169231, 387707, 871989, 1930868, 4215615, 9091410, 19389327, 40944999, 85691893, 177898521, 366614456, 750494796, 1526979694, 3089556090, 6219191608, 12460307373, 24856533408, 49387348955, 97765283686, 192870793594, 379287172272

Offset: 9

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 = 9..4442
• 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.

Programs

PARI

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(s2=sh_euler(sh_euler(x+O(x*x^n))), s3=sh_euler(s2), s4=sh_euler(s3), r3=s3-s2, r4=s4-s3, t8=r4-r3*s3); Vec(t8)} \\ Christian Sievers, May 18 2023

Extensions

More terms from Christian Sievers, May 18 2023