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

%I #5 Jan 01 2020 16:57:07

%S 1,2,4,8,11,18,22,30,36,48,53,67,74,87,100,120,125,145,155,179,193,

%T 215,227,255,273,303,317,339,356,404,416,444,463,506,525,567,592,624,

%U 647,707,725,769,797,833,866,904,928,1008,1026,1086,1125,1171,1189,1247,1283

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

%H Andrew Howroyd, <a href="/A007295/b007295.txt">Table of n, a(n) for n = 1..1000</a>

%F Partial sums of A007203. - _Andrew Howroyd_, Jan 01 2020

%e 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).

%Y Cf. A006546, A007104, A007203.

%K nonn

%O 1,2

%A John Lewis (frc.mass.edu)

%E Terms a(41) and beyond from _Andrew Howroyd_, Jan 01 2020