A396640 Number of geodesics of length n in the braid group B_4.

1, 6, 30, 142, 646, 2870, 12558, 54026, 229338, 963570, 4016674, 16641454, 68614150, 281799158, 1153638466, 4710108514, 19186676438, 78004083510, 316591341866, 1283041428650, 5193053664554, 20994893965398, 84795261908498, 342173680884002, 1379691672165334, 5559241797216166

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Jean Fromentin, Experiments on growth series of braid groups, Journal of Algebra, volume 607, part B, October 2022, pages 232-259. Also preprint arXiv:2009.02054 [math.CO], 2021. See Table 2.

Crossrefs

Cf. A000244 (geodesics in the braid monoid), A396638 (B_3), A396639 (elements of geodesic length).

Sequence in context: A002457 A137400 A220830 * A199938 A285195 A307321

Adjacent sequences: A396637 A396638 A396639 * A396641 A396642 A396643

Keyword

nonn

Author

Ludovic Schwob, Jun 01 2026

Status

approved