cp's OEIS Frontend

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

%I A307236 #21 Apr 19 2019 08:34:54
%S A307236 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,
%T A307236 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,
%U A307236 8,8,12,6,8,16,6,10,2,6,12,10,4,12,5
%N A307236 One half of the number of primitive reduced binary quadratic forms for discriminant 4*A000037(n), for n >= 1.
%C A307236 This is a subset of one half of A082174. See the formula.
%C A307236 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
%F A307236 a(n) = A082174(e(n))/2, with e(n) the position of the n-th even term of A079896.
%e A307236 a(5) = 4 because the fifth even term of A079896 is at position e(5) = 8, and A082174(8)/2 = 4.
%e A307236 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]].
%e A307236 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
%Y A307236 Cf. A000037, A079896, A082174, A307359.
%K A307236 nonn
%O A307236 1,2
%A A307236 _Wolfdieter Lang_, Mar 30 2019