A245747 Number of identity trees with n nodes where the maximal outdegree (branching factor) equals 2.

1, 2, 5, 10, 21, 42, 87, 178, 371, 773, 1630, 3447, 7346, 15712, 33790, 72922, 158020, 343494, 749101, 1638102, 3591723, 7893801, 17387930, 38379199, 84875595, 188036829, 417284180, 927469844, 2064465340, 4601670624, 10270463564, 22950838754, 51346678940

Offset

4,2

Links

Alois P. Heinz, Table of n, a(n) for n = 4..1000

Formula

a(n) = A063895(n+1)-1.

Maple

b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
      `if`(i<1, 0, add(binomial(b(i-1$2, k$2), j)*
       b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
    end:
a:= n-> b(n-1$2, 2$2) -b(n-1$2, 1$2):
seq(a(n), n=4..60);

Mathematica

b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, 1, If[i<1, 0, Sum[Binomial[ b[i-1, i-1, k, k], j]*b[n-i*j, i-1, t - j, k], {j, 0, Min[t, n/i]}]]];
a[n_] :=  b[n-1, n-1, 2, 2] - b[n-1, n-1, 1, 1];
Table[a[n], {n, 4, 60}] (* Jean-François Alcover, Aug 28 2021, after Maple code *)

Crossrefs

Column k=2 of A244523.

Sequence in context: A215410 A279668 A352875 * A032283 A266248 A027437

Adjacent sequences: A245744 A245745 A245746 * A245748 A245749 A245750

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jul 31 2014

Status

approved