A219198 Number of partitions of n into 4 distinct primes.

1, 0, 0, 0, 1, 0, 2, 0, 2, 1, 2, 1, 3, 0, 3, 2, 4, 2, 4, 2, 5, 4, 5, 4, 6, 4, 6, 6, 6, 6, 6, 6, 9, 8, 8, 10, 8, 9, 11, 11, 11, 13, 10, 14, 13, 16, 13, 18, 12, 19, 14, 21, 15, 22, 13, 25, 18, 26, 17, 29, 14, 31, 21, 32, 19, 35, 17, 39, 25, 38, 20, 43, 21, 48, 26

Offset

17,7

Links

Alois P. Heinz, Table of n, a(n) for n = 17..10000

Formula

G.f.: Sum_{0<i_1<i_2<i_3<i_4} x^(Sum_{j=1..4} prime(i_j)).

a(n) = [x^n*y^4] Product_{i>=1} (1+x^prime(i)*y).

Maple

b:= proc(n, i) option remember; `if`(n=0, [1, 0$4], `if`(i<1, [0$5],
       zip((x, y)->x+y, b(n, i-1), [0, `if`(ithprime(i)>n, [0$4],
       b(n-ithprime(i), i-1)[1..4])[]], 0)))
    end:
a:= n-> b(n, numtheory[pi](n))[5]:
seq(a(n), n=17..100);

Mathematica

k = 4; b[n_, i_] := b[n, i] = If[n == 0, Join[{1}, Array[0&, k]], If[i<1, Array[0&, k+1], Plus @@ PadRight[{b[n, i-1], Join[{0}, If[Prime[i]>n, Array[0&, k], Take[b[n-Prime[i], i-1], k]]]}]]]; a[n_] := b[n, PrimePi[n]][[k+1]]; Table[a[n], {n, 17, 100}] (* Jean-François Alcover, Jan 30 2014, after Alois P. Heinz *)

Crossrefs

Column k=4 of A219180.

Sequence in context: A332033 A331981 A099302 * A352513 A025814 A029354

Adjacent sequences: A219195 A219196 A219197 * A219199 A219200 A219201

Keyword

nonn

Author

Alois P. Heinz, Nov 14 2012

Status

approved