A219204 Number of partitions of n into 10 distinct primes.

1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 3, 0, 1, 0, 4, 0, 5, 0, 3, 0, 7, 0, 9, 0, 7, 1, 10, 0, 16, 0, 9, 1, 18, 1, 25, 1, 16, 2, 30, 2, 35, 1, 25, 4, 45, 3, 53, 2, 45, 8, 62, 4, 79, 6, 67, 14, 90, 8, 112, 10, 96, 19, 126, 16, 158, 17, 135, 29, 182, 26, 210

Offset

129,9

Links

Alois P. Heinz, Table of n, a(n) for n = 129..10000

Formula

G.f.: Sum_{0<i_1<i_2<...<i_10} x^(Sum_{j=1..10} prime(i_j)).

a(n) = [x^n*y^10] Product_{i>=1} (1+x^prime(i)*y).

Maple

b:= proc(n, i) option remember; `if`(n=0, [1, 0$10], `if`(i<1, [0$11],
       zip((x, y)->x+y, b(n, i-1), [0, `if`(ithprime(i)>n, [0$10],
       b(n-ithprime(i), i-1)[1..10])[]], 0)))
    end:
a:= n-> b(n, numtheory[pi](n))[11]:
seq(a(n), n=129..210);

Mathematica

k = 10; 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, 129, 210}] (* Jean-François Alcover, Jan 30 2014, after Alois P. Heinz *)

Crossrefs

Column k=10 of A219180.

Sequence in context: A165619 A368118 A328590 * A338264 A353509 A326067

Adjacent sequences: A219201 A219202 A219203 * A219205 A219206 A219207

Keyword

nonn

Author

Alois P. Heinz, Nov 14 2012

Status

approved