A293492 a(n) is the number of sequences (s_1, ..., s_n) of positive integers such that (Product_{k=1..n} [s_k, -1; 1, 0])^2 = [-1, 0; 0, -1].

0, 0, 2, 6, 20, 75, 278

Offset

0,3

Comments

Let M(s) denote the matrix

[s, -1]

[+1, 0]

in SL(2,Z). Then we count sequences of positive integers [s_1, ..., s_n] such that (Product_{k=1..n} M(s_k))^2 = -Identity.

This is Problem III in the Ovsienko article.

Links

Table of n, a(n) for n=0..6.

Valentin Ovsienko, Partitions of unity in SL(2,Z), negative continued fractions, and dissections of polygons, Res. Math. Sci. 5, 21 (2018); arXiv:1710.02996 [math.CO], 2017-2018.

Crossrefs

Cf. A000984 (counts "totally positive" solutions: Sum_k s_k = 3n-3).

Sequence in context: A135588 A395614 A318402 * A150159 A150160 A150161

Adjacent sequences: A293489 A293490 A293491 * A293493 A293494 A293495

Keyword

nonn,more

Author

Michel Marcus, Oct 10 2017

Status

approved