A219199 Number of partitions of n into 5 distinct primes.

1, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 1, 4, 0, 4, 1, 4, 2, 6, 1, 6, 2, 6, 4, 8, 2, 10, 5, 9, 6, 11, 5, 13, 6, 14, 10, 16, 9, 18, 11, 19, 15, 21, 14, 22, 16, 25, 22, 26, 20, 29, 25, 31, 29, 32, 29, 35, 34, 39, 39, 38, 39, 43, 45, 48, 50, 46, 53, 53, 57, 57, 66, 55

Offset

28,7

Links

Alois P. Heinz, Table of n, a(n) for n = 28..10000

Formula

G.f.: Sum_{0<i_1<i_2<...<i_5} x^(Sum_{j=1..5} prime(i_j)).

a(n) = [x^n*y^5] Product_{i>=1} (1+x^prime(i)*y).

Maple

b:= proc(n, i) option remember; `if`(n=0, [1, 0$5], `if`(i<1, [0$6],
       zip((x, y)->x+y, b(n, i-1), [0, `if`(ithprime(i)>n, [0$5],
       b(n-ithprime(i), i-1)[1..5])[]], 0)))
    end:
a:= n-> b(n, numtheory[pi](n))[6]:
seq(a(n), n=28..100);

Mathematica

k = 5; 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, 28, 100}] (* Jean-François Alcover, Jan 30 2014, after Alois P. Heinz *)

Crossrefs

Column k=5 of A219180.

Sequence in context: A329981 A096030 A025815 * A029225 A341977 A309937

Adjacent sequences: A219196 A219197 A219198 * A219200 A219201 A219202

Keyword

nonn

Author

Alois P. Heinz, Nov 14 2012

Status

approved