A062801 Number of 2 X 2 non-singular integer matrices with entries from {0,...,n}.

0, 6, 50, 192, 512, 1126, 2146, 3760, 6112, 9430, 13922, 19888, 27504, 37206, 49202, 63872, 81600, 102854, 127874, 157328, 191440, 230870, 276114, 327776, 386128, 452118, 526178, 608960, 701056, 803430, 916290, 1040976, 1177744, 1327606

Offset: 0

Author

Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 19 2001

Keywords

• nonn
• nice

Comments

All these numbers are even because there are the same number of matrices with positive and negative determinants. [T. D. Noe, Oct 08 2008]

Crossrefs

This sequence a(n) and A059306 give together all the 2 X 2 matrices with entries from {0, ..., n}, i.e. a(n) + A059306(n) = (n+1)^4.

Programs

Mathematica

Table[cnt=0; Do[If[a*d-b*c != 0, cnt++ ], {a,0,n}, {b,0,n}, {c,0,n}, {d,0,n}]; cnt, {n,0,10}] (* T. D. Noe, Oct 08 2008 *)

Extensions

More terms from T. D. Noe, Oct 08 2008