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A176137
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Number of partitions of n into distinct Catalan numbers, cf. A000108.
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11
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1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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0,1
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COMMENTS
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a(n) <= 1;
A197433 gives all such numbers k that a(k) = 1, in other words, this is the characteristic function of A197433, and all three sequences mentioned above are its subsequences. - Antti Karttunen, Jun 25 2014
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LINKS
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FORMULA
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a(n) = f(n,1,1) with f(m,k,c) = if c>m then 0^m else f(m-c,k+1,c') + f(m,k+1,c') where c'=2*c*(2*k+1)/(k+2).
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EXAMPLE
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56 = 42+14 = A000108(5)+A000108(4), all other sums of distinct Catalan numbers are not equal 56, therefore a(56)=1.
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MATHEMATICA
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nmax = 104;
A197433 = CoefficientList[(1/(1 - x))*Sum[ CatalanNumber[k + 1]*x^(2^k)/(1 + x^(2^k)), {k, 0, Log[2, nmax] // Ceiling}] + O[x]^nmax, x];
a[n_] := Boole[MemberQ[A197433, n]];
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PROG
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CROSSREFS
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When right-shifted (prepended with 1) this sequence is the first differences of A244230.
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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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