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

1,3

Comments

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.

Links

Table of n, a(n) for n=1..20.

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.

Example

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

Crossrefs

Cf. A270638.

Sequence in context: A190160 A332052 A088532 * A036621 A001383 A217733

Adjacent sequences: A271361 A271362 A271363 * A271365 A271366 A271367

Keyword

nonn,more

Author

Nathan Fox, Apr 05 2016

Status

approved