A341975 Number of partitions of n into 4 distinct primes (counting 1 as a prime).

1, 0, 1, 0, 1, 1, 2, 0, 2, 1, 3, 2, 4, 2, 4, 3, 5, 4, 5, 3, 5, 6, 7, 6, 6, 7, 8, 9, 9, 10, 7, 10, 9, 12, 10, 12, 9, 15, 12, 16, 13, 18, 12, 20, 14, 22, 16, 23, 13, 27, 16, 29, 19, 30, 14, 33, 19, 36, 21, 35, 15, 43, 23, 43, 23, 43, 18, 52, 26, 51, 26, 52, 21, 64, 29, 58, 28, 64

Offset

11,7

Links

Table of n, a(n) for n=11..88.

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-1)))(
     `if`(i=0, 1, ithprime(i)))+b(n, i-1))), x, 5)
    end:
a:= n-> coeff(b(n, numtheory[pi](n)), x, 4):
seq(a(n), n=11..88);  # 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 - 1]]][
     If[i == 0, 1, Prime[i]]] + b[n, i - 1]]], {x, 0, 5}];
a[n_] := Coefficient[b[n, PrimePi[n]], x, 4];
Table[a[n], {n, 11, 100}] (* Jean-François Alcover, Jul 13 2021, after Alois P. Heinz *)

Crossrefs

Cf. A008578, A036497, A219198, A341947, A341973, A341974, A341976, A341977.

Sequence in context: A029182 A035373 A240138 * A261387 A197317 A035573

Adjacent sequences: A341972 A341973 A341974 * A341976 A341977 A341978

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 24 2021

Status

approved