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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).
1
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
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
KEYWORD
nonn,tabl
AUTHOR
Andrey Zabolotskiy, Feb 10 2020
STATUS
approved