A300440 Number of odd strict trees of weight n (all outdegrees are odd).

1, 1, 1, 1, 1, 2, 2, 3, 5, 7, 11, 18, 27, 45, 75, 125, 207, 353, 591, 1013, 1731, 2984, 5122, 8905, 15369, 26839, 46732, 81850, 142932, 251693, 441062, 778730, 1370591, 2425823, 4281620, 7601359, 13447298, 23919512, 42444497, 75632126, 134454505, 240100289

Offset

1,6

Comments

An odd strict tree of weight n is either a single node of weight n, or a finite odd-length sequence of at least 3 odd strict trees with strictly decreasing weights summing to n.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..500

Example

The a(10) = 7 odd strict trees: 10, (721), (631), (541), (532), ((421)21), ((321)31).

Mathematica

g[n_]:=g[n]=1+Sum[Times@@g/@y, {y, Select[IntegerPartitions[n], Length[#]>1&&OddQ[Length[#]]&&UnsameQ@@#&]}];
Array[g, 20]

Prog

(PARI) seq(n)={my(v=vector(n)); for(n=1, n, v[n] = 1 + polcoef(prod(k=1, n-1, 1 + v[k]*x^k + O(x*x^n)) - prod(k=1, n-1, 1 - v[k]*x^k + O(x*x^n)), n)/2); v} \\ Andrew Howroyd, Aug 25 2018

Crossrefs

Cf. A000009, A000992, A032305, A063834, A078408, A089259, A196545, A273873, A279785, A289501, A298118, A300301, A300352, A300353, A300436, A300439.

Sequence in context: A125189 A226498 A196375 * A147997 A118987 A218557

Adjacent sequences: A300437 A300438 A300439 * A300441 A300442 A300443

Keyword

nonn

Author

Gus Wiseman, Mar 05 2018

Status

approved