A341948 Number of partitions of n into 5 primes (counting 1 as a prime).

1, 1, 2, 2, 4, 4, 6, 5, 8, 6, 10, 7, 12, 9, 15, 10, 18, 12, 21, 14, 25, 15, 29, 18, 33, 21, 37, 20, 41, 23, 46, 26, 51, 27, 58, 31, 63, 34, 68, 33, 77, 39, 83, 42, 90, 43, 101, 48, 107, 53, 116, 52, 128, 58, 134, 61, 142, 61, 157, 68, 165, 73, 176, 73, 194, 82, 201, 84, 211

Offset

5,3

Links

Alois P. Heinz, Table of n, a(n) for n = 5..10000

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, 6)
    end:
a:= n-> coeff(b(n, numtheory[pi](n)), x, 5):
seq(a(n), n=5..73);  # 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, 6}];
a[n_] := Coefficient[b[n, PrimePi[n]], x, 5];
Table[a[n], {n, 5, 73}] (* Jean-François Alcover, Feb 15 2022, after Alois P. Heinz *)

Crossrefs

Cf. A008578, A034891, A259195, A341945, A341946, A341947, A341949, A341950, A341951.

Sequence in context: A211508 A109874 A069345 * A347661 A007730 A330271

Adjacent sequences: A341945 A341946 A341947 * A341949 A341950 A341951

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 24 2021

Status

approved