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A257005 Irregular triangle read by rows: period lengths of periods of Zagier-reduced binary quadratic forms with discriminants D(n) = A079896(n). 1
1, 2, 2, 1, 3, 5, 4, 1, 3, 1, 4, 2, 5, 2, 5, 4, 2, 1, 6, 4, 7, 6, 4, 11, 6, 3, 5, 1, 1, 6, 2, 2, 1, 10, 3, 7, 8, 2, 9, 7, 6, 3, 2, 1, 11, 9, 7, 8, 5, 8, 2, 8, 4, 2, 21, 10, 7, 7, 1, 8, 4, 2, 1, 10, 4, 3, 1, 9, 5, 12, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The possible positive nonsquare discriminants of binary quadratic forms are given in A079896.
For the definition of Zagier-reduced binary quadratic forms, see A257003.
The row sums give A257003(n), the number of Zagier-reduced forms of discriminant D(n).
The number of entries in row n is A256945(n), the class number of primitive forms of discriminant D(n).
REFERENCES
D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.
LINKS
FORMULA
a(n,k), n >= 0, k = 1, 2, ..., A256945(n), is the length of the k-th period of the Zagier-reduced forms for discriminant D(n) = A079896(n). The lengths in row n are organized in nonincreasing order.
EXAMPLE
The table a(n,k) begins:
n/k 1 2 3 4 ... D(n) A256945(n) A257003(n)
0: 1 5 1 1
1: 2 8 1 2
2: 2 1 12 2 3
3: 3 13 1 3
4: 5 17 1 5
5: 4 1 20 2 5
6: 3 1 21 2 4
7: 4 2 24 2 6
8: 5 2 28 2 7
9: 5 29 1 5
10: 4 2 1 32 3 7
11: 6 4 33 2 10
12: 7 37 1 7
13: 6 4 40 2 10
14: 11 41 1 11
15: 6 3 44 2 9
16: 5 1 1 45 3 7
17: 6 2 2 1 48 4 11
18: 10 3 52 2 13
CROSSREFS
Sequence in context: A284644 A079956 A140717 * A160232 A026300 A099514
KEYWORD
nonn,tabf
AUTHOR
Barry R. Smith, Apr 19 2015
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)