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%I #9 Jul 16 2015 22:20:02
%S 0,1,0,0,0,2,0,0,2,1,0,2,2,2,2,3,0,4,6,0,4,5,2,4,6,5,4,7,4,6,10,2,8,
%T 11,2,9,10,6,8,13,6,8,14,8,8,17,8,10,16,7,14,17,10,12,16,11,14,19,12,
%U 12,26,10,14,25,10,19,22,16,16,21,18,20,28,18,18,31,14,23,30,16
%N Number of decompositions of 2n into ordered sums of two odd nonprimes.
%C A002372(n) + A215461(n) + a(n) = n.
%C Note: if n is odd-composite then a(n) is odd, otherwise even.
%C Conjecture: a(n) is never zero for n > 19, verified to 10^9.
%C Conjecture: a(n) > A215461(n) > A002372(n) for sufficiently large n.
%F a(n) = convolve(c,c) where c(n) is the sequence defined by 1 if (2*n+1) is odd nonprime (includes 1), and 0 if (2*n+1) is odd prime.
%e n=15, 2*n=30, 2*n = { 9+21, 15+15, 21+9 }, a(15) = 3.
%e n=18, 2*n=36, 2*n = { 1+35, 9+27, 15+21, 21+15, 27+9, 35+1 }, a(18) = 6.
%Y Cf. A002372, A215461.
%K nonn
%O 0,6
%A _Peter A. Lawrence_, Aug 11 2012