A341462 Number of partitions of n into 4 distinct nonprime parts.

1, 1, 1, 1, 2, 2, 3, 3, 5, 5, 7, 6, 10, 9, 13, 12, 17, 17, 21, 21, 28, 28, 34, 33, 42, 43, 51, 53, 61, 63, 73, 76, 87, 91, 102, 104, 119, 123, 137, 143, 157, 164, 179, 187, 205, 215, 232, 239, 262, 272, 294, 309, 327, 341, 365, 381, 406, 427, 448, 465

Offset

19,5

Links

Table of n, a(n) for n=19..78.

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, 4):
seq(a(n), n=19..78);  # 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]]]];
a[n_] := b[n, n, 4];
Table[a[n], {n, 19, 78}] (* Jean-François Alcover, Jul 13 2021, after Alois P. Heinz *)
Table[Length[Select[IntegerPartitions[n, {4}], Length[#]==Length[ Union[ #]] && NoneTrue[#, PrimeQ]&]], {n, 19, 80}] (* Harvey P. Dale, Nov 07 2021 *)

Crossrefs

Cf. A005171, A018252, A096258, A219198, A302479, A341451, A341461, A341464, A341465, A341466, A341467.

Sequence in context: A086609 A341140 A340285 * A035031 A035032 A121260

Adjacent sequences: A341459 A341460 A341461 * A341463 A341464 A341465

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 12 2021

Status

approved