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 A317100 Number of series-reduced planted achiral trees with n leaves spanning an initial interval of positive integers. 4
 1, 3, 5, 12, 17, 41, 65, 144, 262, 533, 1025, 2110, 4097, 8261, 16407, 32928, 65537, 131384, 262145, 524854, 1048647, 2098181, 4194305, 8390924, 16777234, 33558533, 67109132, 134226070, 268435457, 536887919, 1073741825, 2147516736, 4294968327, 8590000133 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS In these trees, achiral means that all branches directly under any given node that is not a leaf or a cover of leaves are equal, and series-reduced means that every node that is not a leaf or a cover of leaves has at least two branches. LINKS Andrew Howroyd, Table of n, a(n) for n = 1..200 FORMULA a(n) ~ 2^(n-1). - Vaclav Kotesovec, Sep 07 2019 EXAMPLE The a(4) = 12 trees:   (1111), ((11)(11)), (((1)(1))((1)(1))), ((1)(1)(1)(1)),   (1222),   (1122), ((12)(12)),   (1112),   (1233),   (1223),   (1123),   (1234). MATHEMATICA allnorm[n_Integer]:=Function[s, Array[Count[s, y_/; y<=#]+1&, n]]/@Subsets[Range[n-1]+1]; b[n_]:=1+Sum[b[n/d], {d, Rest[Divisors[n]]}]; a[n_]:=Sum[b[GCD@@Length/@Split[ptn]], {ptn, allnorm[n]}]; Array[a, 10] PROG (PARI) seq(n)={my(v=vector(n)); for(n=1, n, v[n]=2^(n-1) + sumdiv(n, d, v[d])); v} \\ Andrew Howroyd, Aug 19 2018 CROSSREFS Cf. A001678, A003238, A052409, A052410, A067824, A167865, A168532, A214577, A289078, A294336, A316782, A317099. Sequence in context: A237351 A299490 A126471 * A199932 A305552 A226652 Adjacent sequences:  A317097 A317098 A317099 * A317101 A317102 A317103 KEYWORD nonn AUTHOR Gus Wiseman, Aug 01 2018 EXTENSIONS Terms a(21) and beyond from Andrew Howroyd, Aug 19 2018 STATUS approved

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Last modified June 4 08:18 EDT 2020. Contains 334825 sequences. (Running on oeis4.)