A181740 Number of sequences of length n over {1, -1} with Erdős discrepancy <= 2.

1, 2, 4, 6, 12, 18, 28, 44, 88, 100, 152, 240, 370, 556, 882, 750, 1500, 2250, 2784, 4284, 6438, 6062, 9526, 14856, 22944, 26164, 39528, 35122, 54800, 80940, 81326, 122422, 244844, 234934, 356154, 309068, 388042, 589796, 900000, 813466, 1212450, 1837030

Offset

0,2

Comments

The Erdős discrepancy of sequence s is defined to be the maximum of the absolute value of s(d) + s(2d) + ... + s(kd) over all k, d such that kd <= n.

a(n) = 0 for all n > A237695(2). - Rainer Rosenthal, Feb 17 2020

Links

Ehit Dinesh Agarwal, Table of n, a(n) for n = 0..60

Boris Konev and Alexei Lisitsa, A SAT attack on the Erdős Discrepancy Conjecture, arXiv:1402.2184 [cs.DM], 2014.

Michael Nielsen, Erdős discrepancy problem

Example

For n = 3 the only sequences omitted are 1 1 1 and -1 -1 -1, so a(3) = 6.

Crossrefs

Cf. A237695.

Sequence in context: A215821 A332284 A192096 * A192224 A167777 A259941

Adjacent sequences: A181737 A181738 A181739 * A181741 A181742 A181743

Keyword

nonn

Author

Jeffrey Shallit, Nov 08 2010

Extensions

a(30)-a(41) from Allan C. Wechsler, Sep 19 2012

Title changed by Rainer Rosenthal, Feb 17 2020

Status

approved