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A007203 Number of elements (a b / c d) in GL(2,Z) with |det| = 1, trace n and 0 <= a <= {b, c} <= d. 3

%I #5 Jan 01 2020 16:57:26

%S 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,

%T 22,17,48,12,28,19,43,19,42,25,32,23,60,18,44,28,36,33,38,24,80,18,60,

%U 39,46,18,58,36,72,29,68,28,76,37,64,34,64,61,72,25,56,34,108

%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="/A007203/b007203.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A006546(n) + A007104(n). - _Andrew Howroyd_, Jan 01 2020

%o (PARI)

%o D(n,s,t)={if(n>=1, sumdiv(n, d, s<=min(d,n/d) && max(d,n/d)<=t), 0)}

%o 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

%Y Cf. A006546, A007104, A007295.

%K nonn

%O 1,3

%A John Lewis (frc.mass.edu)

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

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Last modified April 23 12:08 EDT 2024. Contains 371912 sequences. (Running on oeis4.)