The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A298204 Number of unlabeled rooted trees with n nodes in which all outdegrees are either 0, 1, or 3. 12
 1, 1, 1, 2, 3, 5, 9, 16, 29, 55, 104, 200, 389, 763, 1507, 3002, 6010, 12102, 24484, 49751, 101475, 207723, 426542, 878451, 1813945, 3754918, 7790326, 16196629, 33739335, 70410401, 147187513, 308171861, 646188276, 1356847388, 2852809425, 6005542176 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 Gus Wiseman, Illustration of the first 8 terms. EXAMPLE The a(7) = 9 trees: ((((((o)))))), ((((ooo)))), (((oo(o)))), ((oo((o)))), ((o(o)(o))), (oo(((o)))), (oo(ooo)), (o(o)((o))), ((o)(o)(o)). MAPLE b:= proc(n, i, v) option remember; `if`(n=0,       `if`(v=0, 1, 0), `if`(i<1 or v<1 or n `if`(n<2, n, add(b(n-1\$2, j), j=[1, 3])): seq(a(n), n=1..40);  # Alois P. Heinz, Jan 30 2018 MATHEMATICA multing[n_, k_]:=Binomial[n+k-1, k]; a[n_]:=a[n]=If[n===1, 1, Sum[Product[multing[a[x], Count[ptn, x]], {x, Union[ptn]}], {ptn, Select[IntegerPartitions[n-1], MemberQ[{1, 3}, Length[#]]&]}]]; Table[a[n], {n, 40}] CROSSREFS Cf. A000081, A000598, A001190, A001399, A004111, A014591, A032305, A273873, A292050, A295461, A298118, A298205. Sequence in context: A050253 A198518 A182558 * A265581 A107250 A050168 Adjacent sequences:  A298201 A298202 A298203 * A298205 A298206 A298207 KEYWORD nonn AUTHOR Gus Wiseman, Jan 14 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 10 19:52 EDT 2020. Contains 336381 sequences. (Running on oeis4.)