A332343 Triangle T(n, k) read by rows: number of different infinite-dimensional A-graded algebras with three multiplicative generators of degrees 1, k, n (1 < k < n).

5, 1, 7, 5, 7, 9, 1, 1, 5, 11, 5, 7, 9, 9, 13, 1, 7, 1, 9, 7, 15, 5, 1, 9, 11, 5, 11, 17, 1, 7, 5, 1, 7, 11, 9, 19, 5, 7, 9, 11, 13, 11, 11, 13, 21, 1, 1, 1, 9, 1, 11, 5, 7, 11, 23, 5, 7, 9, 9, 13, 15, 11, 13, 13, 15, 25, 1, 7, 5, 11, 7, 1, 9, 13, 9, 13, 13, 27

Offset

3,1

Links

Table of n, a(n) for n=3..80.

V. I. Arnold, A-graded algebras and continued fractions, Communications on Pure and Applied Mathematics, 42 (1989), 993-1000.

Formula

T(n, k) = A332342(n, k) * 2 + 1 [Arnold].

Example

The triangle begins:
n\k 2  3  4  5  6  7
3|  5
4|  1  7
5|  5  7  9
6|  1  1  5 11
7|  5  7  9  9 13
8|  1  7  1  9  7 15
...

Crossrefs

Cf. A332342.

Sequence in context: A099218 A198129 A244425 * A035109 A301509 A101263

Adjacent sequences: A332340 A332341 A332342 * A332344 A332345 A332346

Keyword

nonn,tabl

Author

Andrey Zabolotskiy, Feb 10 2020

Status

approved