A306201 Number of unlabeled balanced rooted semi-identity trees with n nodes.
0, 1, 1, 2, 3, 4, 6, 8, 12, 16, 25, 35, 53, 77, 117, 173, 265, 396, 605, 919, 1408, 2147, 3305, 5070, 7819, 12049, 18635, 28811, 44672, 69264, 107618, 167292, 260446, 405686, 632743, 987441, 1542555, 2411208, 3772247, 5905002, 9250436, 14499234, 22740910, 35686092
Offset: 0
Keywords
Examples
The a(1) = 1 through a(7) = 8 balanced rooted semi-identity trees:
o (o) (oo) (ooo) (oooo) (ooooo) (oooooo)
((o)) ((oo)) ((ooo)) ((oooo)) ((ooooo))
(((o))) (((oo))) (((ooo))) (((oooo)))
((((o)))) ((o)(oo)) ((o)(ooo))
((((oo)))) ((((ooo))))
(((((o))))) (((o)(oo)))
(((((oo)))))
((((((o))))))
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..500
Crossrefs
Programs
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Mathematica
ursit[n_]:=Join@@Table[Select[Union[Sort/@Tuples[ursit/@ptn]],UnsameQ@@DeleteCases[#,{}]&],{ptn,IntegerPartitions[n-1]}]; Table[Length[Select[ursit[n],SameQ@@Length/@Position[#,{}]&]],{n,10}]
Extensions
More terms from Alois P. Heinz, Jan 29 2019
Comments