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A219200 Number of partitions of n into 6 distinct primes. 5
1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 2, 0, 4, 0, 2, 1, 5, 1, 6, 0, 5, 2, 6, 1, 10, 1, 9, 4, 11, 3, 15, 3, 14, 6, 16, 6, 22, 5, 20, 10, 25, 11, 29, 9, 29, 16, 34, 17, 39, 15, 39, 25, 45, 24, 50, 25, 53, 35, 57, 34, 66, 36, 68, 48, 75, 50, 83, 52, 88, 65, 92, 69, 104 (list; graph; refs; listen; history; text; internal format)
OFFSET

41,7

LINKS

Alois P. Heinz, Table of n, a(n) for n = 41..10000

FORMULA

G.f.: Sum_{0<i_1<i_2<...<i_6} x^(Sum_{j=1..6} prime(i_j)).

a(n) = [x^n*y^6] Product_{i>=1} (1+x^prime(i)*y).

MAPLE

b:= proc(n, i) option remember; `if`(n=0, [1, 0$6], `if`(i<1, [0$7],

       zip((x, y)->x+y, b(n, i-1), [0, `if`(ithprime(i)>n, [0$6],

       b(n-ithprime(i), i-1)[1..6])[]], 0)))

    end:

a:= n-> b(n, numtheory[pi](n))[7]:

seq(a(n), n=41..120);

MATHEMATICA

k = 6; 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, 41, 120}] (* Jean-Fran├žois Alcover, Jan 30 2014, after Alois P. Heinz *)

CROSSREFS

Column k=6 of A219180.

Sequence in context: A156667 A178090 A110914 * A341978 A193527 A127505

Adjacent sequences:  A219197 A219198 A219199 * A219201 A219202 A219203

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 14 2012

STATUS

approved

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Last modified May 16 17:38 EDT 2022. Contains 353719 sequences. (Running on oeis4.)