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A341461
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Number of partitions of n into 3 distinct nonprime parts.
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11
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1, 0, 1, 1, 2, 1, 2, 2, 4, 3, 4, 4, 6, 5, 8, 7, 9, 9, 10, 12, 14, 14, 14, 17, 19, 19, 22, 23, 24, 28, 27, 31, 33, 35, 36, 40, 40, 44, 47, 49, 50, 55, 53, 61, 62, 66, 65, 73, 72, 79, 81, 86, 85, 95, 91, 101, 101, 109, 107, 119, 114, 125, 125, 134, 134
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OFFSET
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11,5
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LINKS
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MAPLE
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b:= proc(n, i, t) option remember; `if`(n=0,
`if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
`if`(isprime(i), 0, b(n-i, min(n-i, i-1), t-1))))
end:
a:= n-> b(n$2, 3):
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MATHEMATICA
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b[n_, i_, t_] := b[n, i, t] = If[n == 0,
If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
If[PrimeQ[i], 0, b[n - i, Min[n - i, i - 1], t - 1]]]];
a[n_] := b[n, n, 3];
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PROG
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(Python)
from functools import lru_cache
from sympy import isprime
@lru_cache(maxsize=None)
def b(n, i, t):
if n == 0: return int(t == 0)
if i < 1 or t < 1: return 0
b2 = 0 if isprime(i) else b(n-i, min(n-i, i-1), t-1)
return b(n, i-1, t) + b2
a = lambda n: b(n, n, 3)
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CROSSREFS
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Cf. A005171, A018252, A096258, A125688, A302479, A341408, A341462, A341464, A341465, A341466, A341467.
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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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