

A215462


Number of decompositions of 2n into ordered sums of two odd nonprimes.


1



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, 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, 12, 26, 10, 14, 25, 10, 19, 22, 16, 16, 21, 18, 20, 28, 18, 18, 31, 14, 23, 30, 16
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OFFSET

0,6


COMMENTS

A002372(n) + A215461(n) + a(n) = n.
Note: if n is oddcomposite then a(n) is odd, otherwise even.
Conjecture: a(n) is never zero for n > 19, verified to 10^9.
Conjecture: a(n) > A215461(n) > A002372(n) for sufficiently large n.


LINKS

Table of n, a(n) for n=0..79.


FORMULA

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.


EXAMPLE

n=15, 2*n=30, 2*n = { 9+21, 15+15, 21+9 }, a(15) = 3.
n=18, 2*n=36, 2*n = { 1+35, 9+27, 15+21, 21+15, 27+9, 35+1 }, a(18) = 6.


CROSSREFS

Cf. A002372, A215461.
Sequence in context: A303907 A290870 A244738 * A025843 A303906 A178580
Adjacent sequences: A215459 A215460 A215461 * A215463 A215464 A215465


KEYWORD

nonn


AUTHOR

Peter A. Lawrence, Aug 11 2012


STATUS

approved



