A219201 Number of partitions of n into 7 distinct primes.

1, 0, 1, 0, 0, 0, 2, 0, 1, 0, 1, 0, 4, 0, 3, 0, 3, 1, 6, 0, 6, 1, 5, 1, 10, 0, 11, 2, 9, 3, 16, 1, 17, 3, 15, 5, 25, 4, 24, 5, 25, 10, 35, 6, 34, 10, 36, 15, 48, 10, 50, 17, 52, 23, 65, 17, 69, 27, 70, 32, 89, 30, 93, 38, 93, 48, 116, 43, 121, 56, 125, 70, 148

Offset

58,7

Links

Alois P. Heinz, Table of n, a(n) for n = 58..10000

Formula

G.f.: Sum_{0<i_1<i_2<...<i_7} x^(Sum_{j=1..7} prime(i_j)).

a(n) = [x^n*y^7] Product_{i>=1} (1+x^prime(i)*y).

Maple

b:= proc(n, i) option remember; `if`(n=0, [1, 0$7], `if`(i<1, [0$8],
       zip((x, y)->x+y, b(n, i-1), [0, `if`(ithprime(i)>n, [0$7],
       b(n-ithprime(i), i-1)[1..7])[]], 0)))
    end:
a:= n-> b(n, numtheory[pi](n))[8]:
seq(a(n), n=58..140);

Mathematica

k = 7; 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, 58, 140}] (* Jean-François Alcover, Jan 30 2014, after Alois P. Heinz *)

Crossrefs

Column k=7 of A219180.

Sequence in context: A159200 A338021 A318721 * A341979 A331838 A361017

Adjacent sequences: A219198 A219199 A219200 * A219202 A219203 A219204

Keyword

nonn

Author

Alois P. Heinz, Nov 14 2012

Status

approved