A209411 Number of 2 x 2 matrices M such that M*transpose(M) == 0 mod n.

1, 4, 1, 16, 49, 4, 1, 64, 81, 196, 1, 16, 337, 4, 49, 256, 577, 324, 1, 784, 1, 4, 1, 64, 1825, 1348, 81, 16, 1681, 196, 1, 1024, 1, 2308, 49, 1296, 2737, 4, 337, 3136, 3361, 4, 1, 16, 3969, 4, 1, 256, 2401, 7300, 577, 5392, 5617, 324, 49, 64, 1

Offset: 1

Author

José María Grau Ribas, Mar 08 2012

Keywords

• nonn
• mult

Links

• Joerg Arndt, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A182039.

Programs

Mathematica

gg[n_] := gg[n] = Flatten[Table[{{x, y}, {z, t}}, {x, n}, {y, n}, {t, n}, {z, n}], 3]; nil[n_] := nil[n] = Length@gg[n][[Select[Range[Length[gg[n]]], Mod[gg[n][[#]].Transpose[gg[n][[#]]], n] == {{0, 0}, {0, 0}} &]]]; Table[Print[nil[n]]; nil[n], {n, 1, 22}]

Extensions

Keyword:mult added by Andrew Howroyd, Aug 02 2018