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A341451
Number of partitions of n into 4 nonprime parts.
10
1, 0, 0, 1, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 6, 5, 7, 8, 9, 10, 13, 13, 17, 17, 22, 21, 27, 27, 34, 34, 41, 40, 51, 49, 62, 59, 71, 70, 86, 82, 101, 97, 117, 112, 135, 131, 155, 150, 180, 170, 202, 196, 228, 222, 259, 248, 291, 281, 324, 314, 361, 348, 404, 388, 445, 431
OFFSET
4,9
MAPLE
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), t-1))))
end:
a:= n-> b(n$2, 4):
seq(a(n), n=4..69); # Alois P. Heinz, Feb 12 2021
MATHEMATICA
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], t - 1]]]];
a[n_] := b[n, n, 4];
Table[a[n], {n, 4, 69}] (* Jean-François Alcover, Aug 19 2021, after Alois P. Heinz *)
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 12 2021
STATUS
approved