A007203 Number of elements (a b / c d) in GL(2,Z) with |det| = 1, trace n and 0 <= a <= {b, c} <= d.

1, 1, 2, 4, 3, 7, 4, 8, 6, 12, 5, 14, 7, 13, 13, 20, 5, 20, 10, 24, 14, 22, 12, 28, 18, 30, 14, 22, 17, 48, 12, 28, 19, 43, 19, 42, 25, 32, 23, 60, 18, 44, 28, 36, 33, 38, 24, 80, 18, 60, 39, 46, 18, 58, 36, 72, 29, 68, 28, 76, 37, 64, 34, 64, 61, 72, 25, 56, 34, 108

Offset

1,3

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Formula

a(n) = A006546(n) + A007104(n). - Andrew Howroyd, Jan 01 2020

Prog

(PARI)
D(n, s, t)={if(n>=1, sumdiv(n, d, s<=min(d, n/d) && max(d, n/d)<=t), 0)}
a(n)={sum(i=0, n\2, my(ad=i*(n-i)); D(ad+1, i, n-i) + D(ad-1, i, n-i))} \\ Andrew Howroyd, Jan 01 2020

Crossrefs

Cf. A006546, A007104, A007295.

Sequence in context: A336165 A011171 A181049 * A354707 A110412 A266285

Adjacent sequences: A007200 A007201 A007202 * A007204 A007205 A007206

Keyword

nonn

Author

John Lewis (frc.mass.edu)

Extensions

Terms a(41) and beyond from Andrew Howroyd, Jan 01 2020

Status

approved