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%I #12 Apr 05 2016 23:05:37
%S 1,1,2,4,8,15,29,52,93,162,279,463,769,1236,1975,3100,4824,7358,11200,
%T 16706
%N Number of novel integer partitions whose parts sum to 2n.
%C A novel integer partition is an integer partition with k parts with overall gcd 1 such that there are k-1 linearly independent ways to add up the parts with plus or minus signs and reach zero.
%C For a novel integer partition, it is always possible to add up the parts with plus or minus signs and reach zero. For this reason, no odd number can be the sum of a novel partition.
%H R. Arratia and S. DeSalvo, <a href="http://arxiv.org/abs/1105.2834">On the singularity of random Bernoulli matrices -- novel integer partitions and lower bound expansions</a>, arXiv:1105.2834 [math.PR], 2001-2012.
%H R. Arratia and S. DeSalvo, <a href="http://dx.doi.org/10.1007/s00026-013-0176-7">On the singularity of random Bernoulli matrices -- novel integer partitions and lower bound expansions</a>, Annals of Combinatorics, 17(2) (2013), 251--274.
%e 111111 and 21111 are both novel partitions, and they both sum to 6. No other novel partition sums to 6, so, a(3)=2.
%Y Cf. A270638.
%K nonn,more
%O 1,3
%A _Nathan Fox_, Apr 05 2016