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A219202 Number of partitions of n into 8 distinct primes. 4
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Jan 30 2014, after Alois P. Heinz *)

CROSSREFS

Column k=8 of A219180.

Sequence in context: A240672 A243016 A284975 * A341980 A218031 A135523

Adjacent sequences:  A219199 A219200 A219201 * A219203 A219204 A219205

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 14 2012

STATUS

approved

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Last modified June 12 14:15 EDT 2021. Contains 344956 sequences. (Running on oeis4.)