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 A300353 Number of strict trees of weight n with odd leaves. 7
 1, 1, 0, 1, 1, 2, 2, 4, 7, 14, 24, 46, 92, 186, 368, 750, 1529, 3160, 6510, 13590, 28374, 59780, 125732, 266468, 564188, 1202842, 2560106, 5484304, 11732400, 25229068, 54187918, 116938702, 252039411, 545593378, 1179545874, 2560009400, 5550315640, 12075064432 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS This sequence is initially dominated by A300352 but eventually becomes much greater. A strict tree of weight n > 0 is either a single node of weight n, or a sequence of two or more strict trees with strictly decreasing weights summing to n. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..500 FORMULA O.g.f: (1 + x/(1-x^2) + Product_{i>0} (1 + a(i)x^i))/2. a(n) = Sum_{i=1..A000009(n)} A294018(A300351(n,i)). EXAMPLE The a(8) = 7 strict trees with odd leaves: (71), (53), (((51)1)1), (((31)3)1), (((31)1)3), ((31)31), ((((31)1)1)1)1). MATHEMATICA d[n_]:=d[n]=If[EvenQ[n], 0, 1]+Sum[Times@@d/@y, {y, Select[IntegerPartitions[n], Length[#]>1&&UnsameQ@@#&]}]; Table[d[n], {n, 40}] PROG (PARI) seq(n)={my(v=vector(n)); v[1]=1; for(n=2, n, v[n] = polcoef(x/(1-x^2) + prod(k=1, n-1, 1 + v[k]*x^k + O(x*x^n)), n)); concat([1], v)} \\ Andrew Howroyd, Aug 25 2018 CROSSREFS Cf. A000009, A063834, A078408, A089259, A196545, A279374, A279785, A289501, A294018, A294079, A299203, A300300, A300301, A300351, A300352, A300354, A300355. Sequence in context: A067953 A109070 A169973 * A049868 A120363 A118988 Adjacent sequences: A300350 A300351 A300352 * A300354 A300355 A300356 KEYWORD nonn AUTHOR Gus Wiseman, Mar 03 2018 STATUS approved

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Last modified April 18 16:22 EDT 2024. Contains 371780 sequences. (Running on oeis4.)