A000251 Number of trees of diameter 6. (Formerly M2887 N1158)

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

7,2

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

Prog

(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

Crossrefs

Cf. A034853, A000550 (diameter 7).

Sequence in context: A188475 A072610 A110954 * A159229 A239713 A122023

Adjacent sequences: A000248 A000249 A000250 * A000252 A000253 A000254

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Nov 21 2010

Status

approved