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A341467
Number of partitions of n into 8 distinct nonprime parts.
9
1, 1, 1, 1, 2, 2, 4, 5, 6, 7, 10, 12, 16, 19, 24, 28, 36, 41, 52, 60, 73, 85, 102, 116, 142, 161, 192, 217, 256, 287, 339, 382, 442, 496, 574, 639, 737, 821, 937, 1041, 1184, 1309, 1483, 1640, 1845, 2037, 2283, 2508, 2807, 3081, 3430, 3761, 4170, 4553, 5045
OFFSET
64,5
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, 8):
seq(a(n), n=64..118); # 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, 8];
Table[a[n], {n, 64, 118}] (* Jean-François Alcover, Feb 22 2022, after Alois P. Heinz *)
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 12 2021
STATUS
approved