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A300440
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Number of odd strict trees of weight n (all outdegrees are odd).
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5
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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
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OFFSET
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1,6
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COMMENTS
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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.
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LINKS
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EXAMPLE
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The a(10) = 7 odd strict trees: 10, (721), (631), (541), (532), ((421)21), ((321)31).
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MATHEMATICA
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g[n_]:=g[n]=1+Sum[Times@@g/@y, {y, Select[IntegerPartitions[n], Length[#]>1&&OddQ[Length[#]]&&UnsameQ@@#&]}];
Array[g, 20]
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PROG
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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^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
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CROSSREFS
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Cf. A000009, A000992, A032305, A063834, A078408, A089259, A196545, A273873, A279785, A289501, A298118, A300301, A300352, A300353, A300436, A300439.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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