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A219198 Number of partitions of n into 4 distinct primes. 5
1, 0, 0, 0, 1, 0, 2, 0, 2, 1, 2, 1, 3, 0, 3, 2, 4, 2, 4, 2, 5, 4, 5, 4, 6, 4, 6, 6, 6, 6, 6, 6, 9, 8, 8, 10, 8, 9, 11, 11, 11, 13, 10, 14, 13, 16, 13, 18, 12, 19, 14, 21, 15, 22, 13, 25, 18, 26, 17, 29, 14, 31, 21, 32, 19, 35, 17, 39, 25, 38, 20, 43, 21, 48, 26 (list; graph; refs; listen; history; text; internal format)
OFFSET

17,7

LINKS

Alois P. Heinz, Table of n, a(n) for n = 17..10000

FORMULA

G.f.: Sum_{0<i_1<i_2<i_3<i_4} x^(Sum_{j=1..4} prime(i_j)).

a(n) = [x^n*y^4] Product_{i>=1} (1+x^prime(i)*y).

MAPLE

b:= proc(n, i) option remember; `if`(n=0, [1, 0$4], `if`(i<1, [0$5],

       zip((x, y)->x+y, b(n, i-1), [0, `if`(ithprime(i)>n, [0$4],

       b(n-ithprime(i), i-1)[1..4])[]], 0)))

    end:

a:= n-> b(n, numtheory[pi](n))[5]:

seq(a(n), n=17..100);

MATHEMATICA

k = 4; 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, 17, 100}] (* Jean-Fran├žois Alcover, Jan 30 2014, after Alois P. Heinz *)

CROSSREFS

Column k=4 of A219180.

Sequence in context: A332033 A331981 A099302 * A025814 A029354 A035434

Adjacent sequences:  A219195 A219196 A219197 * A219199 A219200 A219201

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 14 2012

STATUS

approved

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Last modified January 20 08:54 EST 2022. Contains 350471 sequences. (Running on oeis4.)