A007295 Number of elements (a b, c d) in GL(2,Z) with |det| = 1, trace <= n and 0 <= a <= {b, c} <= d.

1, 2, 4, 8, 11, 18, 22, 30, 36, 48, 53, 67, 74, 87, 100, 120, 125, 145, 155, 179, 193, 215, 227, 255, 273, 303, 317, 339, 356, 404, 416, 444, 463, 506, 525, 567, 592, 624, 647, 707, 725, 769, 797, 833, 866, 904, 928, 1008, 1026, 1086, 1125, 1171, 1189, 1247, 1283

Offset

1,2

Links

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

Formula

Partial sums of A007203. - Andrew Howroyd, Jan 01 2020

Example

Example from Neven Juric, Apr 21 2008: a(5) = 11 from the matrices (0 1, 1 1), (0 1, 1 2), (0 1, 1 3), (0 1, 1 4), (0 1, 1 5), (1 1, 1 2), (1 1, 2 3), (1 1, 3 4), (1 2, 1 3), (1 2, 2 3), (1 3, 1 4).

Crossrefs

Cf. A006546, A007104, A007203.

Sequence in context: A010068 A295674 A120632 * A053439 A337501 A365922

Adjacent sequences: A007292 A007293 A007294 * A007296 A007297 A007298

Keyword

nonn

Author

John Lewis (frc.mass.edu)

Extensions

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

Status

approved