A270638 -id:A270638 - cp's OEIS frontend

A271364 Number of novel integer partitions whose parts sum to 2n.

1, 1, 2, 4, 8, 15, 29, 52, 93, 162, 279, 463, 769, 1236, 1975, 3100, 4824, 7358, 11200, 16706

Offset: 1

Nathan Fox, Apr 05 2016

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.

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.

			111111 and 21111 are both novel partitions, and they both sum to 6. No other novel partition sums to 6, so, a(3)=2.

R. Arratia and S. DeSalvo, On the singularity of random Bernoulli matrices -- novel integer partitions and lower bound expansions, arXiv:1105.2834 [math.PR], 2001-2012.
R. Arratia and S. DeSalvo, On the singularity of random Bernoulli matrices -- novel integer partitions and lower bound expansions, Annals of Combinatorics, 17(2) (2013), 251--274.

Cf. A270638.

cp's OEIS Frontend

A271364 Number of novel integer partitions whose parts sum to 2n.

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