A059306 - OEIS

%I #19 Nov 29 2016 08:00:11

%S 1,10,31,64,113,170,255,336,449,570,719,848,1057,1210,1423,1664,1921,

%T 2122,2447,2672,3041,3386,3727,4000,4497,4858,5263,5696,6225,6570,

%U 7231,7600,8177,8730,9263,9872,10689,11130,11727,12384,13265,13754,14703

%N Number of 2 X 2 singular integer matrices with elements from {0,...,n}.

%H Vincenzo Librandi and Chai Wah Wu, <a href="/A059306/b059306.txt">Table of n, a(n) for n = 0..10000</a> (terms for n = 0..100 from Vincenzo Librandi)

%F a(n) = A134506(n) + (2n+1)^2. Shi's result (see formula section in A134506) shows that a(n) = kn^2 log n + cn^2 + O(n^e) where k = 12/Pi^2, e > 547/416 = 1.3149..., and c = 4.5113... - _Chai Wah Wu_, Nov 28 2016

%t a[0] = 1; a[n_] := Table[{w, x, y, z} /. {ToRules[ Reduce[0 <= x <= n && 0 <= y <= n && 0 <= z <= n && w*z - x*y == 0, {x, y, z}, Integers]] }, {w, 0, n}] // Flatten[#, 1]& // Length; Table[Print[an = a[n]]; an, {n, 0, 42}] (* _Jean-François Alcover_, Oct 11 2013 *)

%Y Cf. A062801, A134506.

%K nonn,nice

%O 0,2

%A _John W. Layman_, Jan 25 2001

%E More terms from Larry Reeves (larryr(AT)acm.org), Jan 09 2003