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A102291
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Total number of prime parts in all compositions of n.
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10
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0, 0, 1, 3, 7, 18, 42, 98, 222, 497, 1100, 2413, 5250, 11350, 24398, 52193, 111180, 235949, 499074, 1052502, 2213710, 4644833, 9724492, 20318637, 42376578, 88231765, 183420748, 380755932, 789340736, 1634339217, 3379993922, 6982618822, 14410499598, 29711523105
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OFFSET
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0,4
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LINKS
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FORMULA
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G.f.: Sum_{k>=1} x^prime(k)*(1-x)^2/(1-2*x)^2.
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 0, add(a(n-j)+
`if`(isprime(j), ceil(2^(n-j-1)), 0), j=1..n))
end:
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MATHEMATICA
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a[n_] := a[n] = If[n==0, 0, Sum[a[n-j] + If[PrimeQ[j], Ceiling[2^(n-j-1)], 0], {j, 1, n}]];
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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