[seqfan] Recursions for numbers of Goldbach, Chen and Lemoine-Levy partitions

[Vladimir Shevelev]

Dear SeqFans,

Since in my arXiv paper 0901.3102, examples 2-3 there are some technical errors, here I give all recursions for numbers of Goldbach, Chen and Lemoine-Levy partitions.
1) Goldbach partitions (A002375):
a(1)=0; for n>=2, a(n) = sum{3<=p<=n, p is prime}A(2*n - p) - Binom(A(n),2) - a(n-1) - a(n-2) - ... -a(1), where A(n) = A033270(n);
2) Chen partitions (A155216):
a(1)=0; for n>=2, a(n) = sum{3<=p<=n, p prime}A(2*n - p) + sum{t<=2*n, t odd semiprime}A(2*n - t) + A(n) - Binom(A(n),2) + delta(n) - a(n-1) - ... - a(1), where A(n) = A033270(n), delta(n) = 1, if n is prime, and delta(n) = 2, if n is composite number;
3)Lemoine-Levy partitions(A046927):
a(0)=0; for n>=1, a(n) = sum{3<=p<=n+1, p prime}A((2*n + 1 - p)/2) + sum{2<=q<=(n+1)/2, q prime}B(2*n + 1 - 2*q) - A((n+1)/2)*B(n+1) - a(n-1) - ... - a(0), where A(n) = A000720(n), B(n) = A033270(n). 

Best regards,
Vladimir

 Shevelev Vladimir‎