A070757 Number of ways to write 4n as a sum of 4 primes.

0, 1, 2, 3, 6, 7, 11, 13, 15, 21, 24, 26, 34, 38, 41, 50, 56, 57, 70, 77, 81, 96, 100, 109, 126, 129, 138, 156, 163, 175, 199, 198, 211, 239, 241, 258, 283, 281, 308, 335, 335, 360, 382, 385, 421, 445, 437, 482, 508, 503, 556, 571, 561, 632, 657, 645, 705, 726

Offset: 1

Author

Benoit Cloitre, May 14 2002

Keywords

• nonn
• look

Examples

			4*3 = 12 = 2+2+3+5 = 3+3+3+3 hence a(3)=2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A259194.

Programs

Maple

N:= 400: # to get a(0) to a(N/4)
Primes:= select(isprime, [$1..N]):
np:= nops(Primes):
for j from 0 to np do g[0, j]:= 1 od:
for n from 1 to 4 do
  g[n, 0]:= 0:
  for j from 1 to np do
     g[n, j]:= convert(series(add(g[k, j-1]
          *x^((n-k)*Primes[j]), k=0..n), x, N+1), polynom)
  od
od:
seq(coeff(g[4, np], x, 4*i), i=1..N/4); # Robert Israel, Oct 29 2019

PARI

a(n)={my(s=0); forprime(i=2, n, forprime(j=i, (4*n-i)\3, forprime(k=j, (4*n-i-j)\2, if(isprime(4*n-i-j-k), s++)))); s} \\ Andrew Howroyd, Oct 29 2019

Formula

a(n) = A259194(4*n). - Robert Israel, Oct 29 2019

Extensions

Corrected by Robert Israel, Oct 29 2019