A245749 Number of identity trees with n nodes where the maximal outdegree (branching factor) equals 4.

2, 6, 21, 63, 185, 512, 1403, 3750, 9928, 25969, 67462, 174039, 446884, 1142457, 2911078, 7396049, 18746761, 47420345, 119746936, 301941284, 760387426, 1912814031, 4807298905, 12071798139, 30292240853, 75965728619, 190398931985, 476980247827, 1194401725174

Offset

11,1

Links

Alois P. Heinz, Table of n, a(n) for n = 11..1000

Formula

a(n) = A116380(n) - A116379(n).

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, 4$2) -b(n-1$2, 3$2):
seq(a(n), n=11..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, 4, 4] - b[n-1, n-1, 3, 3];
Table[a[n], {n, 11, 60}] (* Jean-François Alcover, Aug 28 2021, after Maple code *)

Crossrefs

Column k=4 of A244523.

Sequence in context: A088812 A228398 A228394 * A342440 A001434 A119098

Adjacent sequences: A245746 A245747 A245748 * A245750 A245751 A245752

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jul 31 2014

Status

approved