A219204 - OEIS

%I #13 Sep 21 2015 19:39:19

%S 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,

%T 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,

%U 90,8,112,10,96,19,126,16,158,17,135,29,182,26,210

%N Number of partitions of n into 10 distinct primes.

%H Alois P. Heinz, <a href="/A219204/b219204.txt">Table of n, a(n) for n = 129..10000</a>

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

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

%p b:= proc(n, i) option remember; `if`(n=0, [1,0$10], `if`(i<1, [0$11],

%p        zip((x, y)->x+y, b(n, i-1), [0, `if`(ithprime(i)>n, [0$10],

%p        b(n-ithprime(i), i-1)[1..10])[]], 0)))

%p     end:

%p a:= n-> b(n, numtheory[pi](n))[11]:

%p seq(a(n), n=129..210);

%t 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_ *)

%Y Column k=10 of A219180.

%K nonn

%O 129,9

%A _Alois P. Heinz_, Nov 14 2012