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A245749
Number of identity trees with n nodes where the maximal outdegree (branching factor) equals 4.
2
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
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
KEYWORD
nonn
AUTHOR
Joerg Arndt and Alois P. Heinz, Jul 31 2014
STATUS
approved