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A341457
Number of partitions of n into 9 nonprime parts.
10
1, 0, 0, 1, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 6, 6, 7, 9, 10, 12, 15, 17, 20, 24, 28, 32, 38, 44, 51, 60, 67, 79, 91, 104, 120, 138, 154, 180, 203, 232, 262, 300, 335, 385, 428, 489, 543, 620, 688, 782, 861, 979, 1078, 1222, 1341, 1518, 1661, 1875, 2048, 2308
OFFSET
9,9
LINKS
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, 9):
seq(a(n), n=9..68); # 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], 0]]];
a[n_] := b[n, n, 9];
Table[a[n], {n, 9, 68}] (* Jean-François Alcover, Feb 23 2022, after Alois P. Heinz *)
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 12 2021
STATUS
approved