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A244230
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a(n) is the least k such that A197433(k) >= n.
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7
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0, 1, 2, 3, 4, 4, 5, 6, 7, 8, 8, 8, 8, 8, 8, 9, 10, 11, 12, 12, 13, 14, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 18, 19, 20, 20, 21, 22, 23, 24, 24, 24, 24, 24, 24, 25, 26, 27, 28, 28, 29, 30, 31, 32, 32, 32, 32
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OFFSET
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0,3
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COMMENTS
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For n >= 1, a(n) is the total number of ways the natural numbers in range 1 .. n can be represented as sums of distinct Catalan numbers (A000108). Note that for any one number, number of such solutions may be at most one. In other words, this sequence is one less than the partial sums of A176137 (number of partitions of n into distinct Catalan numbers).
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LINKS
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FORMULA
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For all n >= 0, a(A197433(n)) = n. [This works as an inverse function for the injection A197433].
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MATHEMATICA
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nmax = 68;
A197433[n_] := If[n == 0, 0, SeriesCoefficient[(1/(1-x))*Sum[ CatalanNumber[k+1]*x^(2^k)/(1+x^(2^k)), {k, 0, Log[2, n] // Ceiling}], {x, 0, n}]];
a[n_] := For[k = 0, True, k++, If[A197433[k] >= n, Return[k]]];
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PROG
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CROSSREFS
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The first differences give A176137 from its term a(1) onward.
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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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