A219202 Number of partitions of n into 8 distinct primes.

1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 3, 0, 1, 0, 3, 0, 5, 0, 4, 1, 5, 0, 10, 0, 6, 1, 10, 1, 15, 1, 10, 2, 17, 2, 23, 1, 17, 5, 27, 4, 32, 2, 30, 9, 38, 7, 48, 6, 43, 13, 56, 10, 70, 12, 62, 20, 78, 19, 98, 20, 86, 31, 109, 30, 128, 28, 121, 49, 145, 45, 170

Offset

77,11

Links

Alois P. Heinz, Table of n, a(n) for n = 77..10000

Formula

G.f.: Sum_{0<i_1<i_2<...<i_8} x^(Sum_{j=1..8} prime(i_j)).

a(n) = [x^n*y^8] Product_{i>=1} (1+x^prime(i)*y).

Maple

b:= proc(n, i) option remember; `if`(n=0, [1, 0$8], `if`(i<1, [0$9],
       zip((x, y)->x+y, b(n, i-1), [0, `if`(ithprime(i)>n, [0$8],
       b(n-ithprime(i), i-1)[1..8])[]], 0)))
    end:
a:= n-> b(n, numtheory[pi](n))[9]:
seq(a(n), n=77..150);

Mathematica

k = 8; 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, 77, 150}] (* Jean-François Alcover, Jan 30 2014, after Alois P. Heinz *)

Crossrefs

Column k=8 of A219180.

Sequence in context: A352288 A243016 A284975 * A341980 A218031 A135523

Adjacent sequences: A219199 A219200 A219201 * A219203 A219204 A219205

Keyword

nonn

Author

Alois P. Heinz, Nov 14 2012

Status

approved