A307236 One half of the number of primitive reduced binary quadratic forms for discriminant 4*A000037(n), for n >= 1.

1, 2, 1, 2, 4, 2, 4, 2, 2, 5, 4, 4, 1, 2, 6, 2, 6, 6, 4, 6, 4, 2, 4, 5, 6, 8, 4, 4, 10, 4, 7, 2, 8, 6, 3, 4, 10, 8, 6, 12, 4, 4, 4, 8, 6, 5, 6, 8, 6, 6, 12, 6, 10, 11, 4, 4, 6, 8, 10, 2, 8, 10, 8, 8, 7, 8, 8, 12, 6, 8, 16, 6, 10, 2, 6, 12, 10, 4, 12, 5

Offset

1,2

Comments

This is a subset of one half of A082174. See the formula.

This sequence is also one half of the total length of the A307359(n) cycles for discriminant 4*D(n), with D(n) = A000037(n). See the W. Lang link in A324251, Table 2, last column SigmaL(n) = 2*a(n). - Wolfdieter Lang, Apr 19 2019

Links

Table of n, a(n) for n=1..80.

Formula

a(n) = A082174(e(n))/2, with e(n) the position of the n-th even term of A079896.

Example

a(5) = 4 because the fifth even term of A079896 is at position e(5) = 8, and A082174(8)/2 = 4.
The 2*a(5) = 8 primitive reduced forms for discriminant 4*A000037(5) = 4*7 = 28 are [[-2, 2, 3], [2, 2, -3], [-3, 2, 2], [3, 2, -2], [-1, 4, 3], [1, 4, -3], [-3, 4, 1], [3, 4, -1]].
The preceding 8 forms give the 2 = A307359(5) 4-cycles CR(5) = [[1, 4, -3], [-3, 2, 2], [2, 2, -3], [-3, 4, 1]], the principal cycle with the principal reduced form [1, 4, -3], and the 4-cycle obtained from this by a sign flip of the outer form entries. - Wolfdieter Lang, Apr 19 2019

Crossrefs

Cf. A000037, A079896, A082174, A307359.

Sequence in context: A180108 A300417 A121339 * A324382 A234359 A099500

Adjacent sequences: A307233 A307234 A307235 * A307237 A307238 A307239

Keyword

nonn

Author

Wolfdieter Lang, Mar 30 2019

Status

approved