A300797 Number of strict trees of weight 2n + 1 in which all outdegrees and all leaves are odd.
1, 1, 1, 1, 2, 2, 4, 6, 11, 17, 34, 59, 118, 213, 424, 799, 1606, 3072, 6216, 12172, 24650, 48710, 99333, 198237, 405526, 815267, 1673127, 3387165, 6974702, 14179418, 29285048, 59841630, 123848399, 253927322, 526936694, 1084022437, 2253778793, 4649778115
Offset: 0
Keywords
Examples
The a(7) = 6 strict trees: 15, (11 3 1), (9 5 1), (7 5 3), ((7 3 1) 3 1), ((5 3 1) 5 1).
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..500
Crossrefs
Programs
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Mathematica
a[n_]:=a[n]=If[OddQ[n],1,0]+Sum[Times@@a/@ptn,{ptn,Select[IntegerPartitions[n],Length[#]>1&&OddQ[Length[#]]&&UnsameQ@@#&]}]; Table[a[n],{n,1,60,2}]
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PARI
seq(n)={my(v=vector(n)); for(n=1, n, v[n] = 1 + polcoef(prod(k=1, n-1, 1 + v[k]*x^(2*k-1) + O(x^(2*n))) - prod(k=1, n-1, 1 - v[k]*x^(2*k-1) + O(x^(2*n))), 2*n-1)/2); v} \\ Andrew Howroyd, Aug 26 2018
Extensions
a(30)-a(37) from Alois P. Heinz, Mar 13 2018
Comments