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URL: https://oeis.org/A341466

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A341466
Number of partitions of n into 7 distinct nonprime parts.
9
1, 0, 1, 1, 2, 2, 4, 3, 6, 6, 9, 9, 14, 15, 21, 23, 30, 33, 43, 47, 61, 67, 81, 91, 112, 123, 150, 165, 194, 217, 255, 281, 330, 363, 417, 461, 529, 582, 665, 730, 823, 905, 1018, 1115, 1253, 1368, 1519, 1662, 1844, 2010, 2227, 2419, 2659, 2894, 3175, 3442
OFFSET
50,5
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-1), t-1))))
end:
a:= n-> b(n$2, 7):
seq(a(n), n=50..105); # 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 - 1], t - 1], 0]]];
a[n_] := b[n, n, 7];
Table[a[n], {n, 50, 105}] (* Jean-François Alcover, Feb 23 2022, after Alois P. Heinz *)
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 12 2021
STATUS
approved