A341946 Number of partitions of n into 3 primes (counting 1 as a prime).

1, 1, 2, 2, 3, 2, 4, 2, 4, 2, 4, 2, 6, 3, 6, 2, 6, 3, 8, 3, 8, 3, 9, 4, 10, 3, 9, 2, 10, 4, 12, 3, 12, 4, 13, 4, 13, 3, 14, 3, 15, 5, 16, 4, 17, 4, 18, 6, 19, 4, 19, 3, 20, 6, 20, 3, 20, 4, 23, 7, 23, 4, 26, 5, 26, 6, 23, 3, 27, 5, 28, 7, 28, 6, 33, 5, 31, 7, 30, 5, 34

Offset: 3

Author

Ilya Gutkovskiy, Feb 24 2021

Keywords

• nonn
• look

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..10000

Crossrefs

Cf. A008578, A034891, A068307, A341945, A341947, A341948, A341949, A341950, A341951.

Programs

Maple

b:= proc(n, i) option remember; series(`if`(n=0, 1,
     `if`(i<0, 0, (p-> `if`(p>n, 0, x*b(n-p, i)))(
     `if`(i=0, 1, ithprime(i)))+b(n, i-1))), x, 4)
    end:
a:= n-> coeff(b(n, numtheory[pi](n)), x, 3):
seq(a(n), n=3..83);  # Alois P. Heinz, Feb 24 2021

Mathematica

b[n_, i_] := b[n, i] = Series[If[n == 0, 1,
     If[i < 0, 0, Function[p, If[p > n, 0, x*b[n - p, i]]][
     If[i == 0, 1, Prime[i]]] + b[n, i-1]]], {x, 0, 4}];
a[n_] := Coefficient[b[n, PrimePi[n]], x, 3];
Table[a[n], {n, 3, 83}] (* Jean-François Alcover, Feb 14 2022, after Alois P. Heinz *)