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A348588
Number of partitions of n into 3 parts with at least 1 prime part.
0
0, 0, 0, 0, 1, 2, 2, 4, 4, 6, 7, 8, 10, 12, 13, 17, 17, 19, 22, 25, 26, 31, 31, 36, 37, 42, 43, 49, 49, 56, 56, 64, 63, 72, 70, 80, 79, 87, 87, 99, 94, 107, 105, 116, 114, 126, 123, 139, 134, 148, 145, 158, 155, 173, 166, 184, 178, 195, 189, 211, 202, 222, 215, 236, 226, 250, 242
OFFSET
0,6
FORMULA
a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} sign(c(i) + c(j) + c(n-i-j)), where c is the prime characteristic (A010051).
MAPLE
b:= proc(n, i, t) option remember; series(
`if`(n=0, t, `if`(i<1, 0, expand(x*b(n-i, min(n-i, i),
`if`(isprime(i), 1, t)))+b(n, i-1, t))), x, 4)
end:
a:= n-> coeff(b(n$2, 0), x, 3):
seq(a(n), n=0..66); # Alois P. Heinz, Oct 24 2021
MATHEMATICA
Table[Length@Select[IntegerPartitions[k, {3}], Or@@PrimeQ@#&], {k, 0, 66}] (* Giorgos Kalogeropoulos, Oct 24 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Oct 24 2021
STATUS
approved