This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
(See the Mathematica section at A209978.)
a(2)=11 counts these (w,x,y,z): (1,1,1,1), (1,1,1,2), (1,1,2,1), (2,1,2,1), (2,1,1,2), (1,2,2,1), (1,2,1,2), (1,1,2,2), (1,2,2,2), (2,1,2,2), (2,2,2,2).
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w*x < 2 y*z, s = s + 1], {w, 1, #},
{x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]] (* A211795 *)
(* Peter J. C. Moses, Apr 13 2012 *)
a(2)=6 counts these matrices (using reduced matrix notation): (1,0,0,1), determinant = 1, inverse = (1,0,0,1) (1,0,1,1), determinant = 1, inverse = (1,0,-1,1) (1,1,0,1), determinant = 1, inverse = (1,-1,0,1) (0,1,1,0), determinant = -1, inverse = (0,1,1,0) (0,1,1,1), determinant = -1, inverse = (-1,1,1,0) (1,1,1,0), determinant = -1, inverse = (0,1,1,-1)
a = 0; b = n; z1 = 50;
t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
c[n_, k_] := c[n, k] = Count[t[n], k]
Table[c[n, 0], {n, 0, z1}] (* A059306 *)
Table[c[n, 1], {n, 0, z1}] (* A171503 *)
2 % (* A210000 *)
Table[c[n, 2], {n, 0, z1}] (* A209973 *)
%/4 (* A209974 *)
Table[c[n, 3], {n, 0, z1}] (* A209975 *)
Table[c[n, 4], {n, 0, z1}] (* A209976 *)
Table[c[n, 5], {n, 0, z1}] (* A209977 *)
a:= proc(n) option remember; `if`(n<2, 0,
a(n-1)-1 + 2*numtheory[phi](n))
end:
seq(a(n), n=0..60); # Alois P. Heinz, May 05 2020
a = 1; b = n; z1 = 50;
t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
c[n_, k_] := c[n, k] = Count[t[n], k]
Table[c[n, 0], {n, 0, z1}] (* A134506 *)
Table[c[n, 1], {n, 0, z1}] (* A196227 *)
%/2 (* A209978 *)
Table[2 c[n, 1], {n, 0, z1}](* A209979 *)
Table[c[n, 2], {n, 0, z1}] (* A197168 *)
%/2 (* A209980 *)
Table[c[n, 3], {n, 0, z1}] (* A210001 *)
Table[c[n, 4], {n, 0, z1}] (* A210002 *)
Table[c[n, 5], {n, 0, z1}] (* A210027 *)
(See the Mathematica section at A210000.)
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