A197168 Number of 2 X 2 integer matrices with elements from {1,...,n} whose determinant is 2.

0, 0, 2, 6, 18, 30, 50, 70, 98, 118, 162, 198, 226, 270, 338, 366, 426, 486, 554, 622, 682, 726, 842, 926, 986, 1062, 1202, 1270, 1362, 1470, 1562, 1678, 1802, 1878, 2066, 2158, 2250, 2390, 2602, 2694, 2818, 2974, 3114, 3278, 3434, 3526, 3786, 3966, 4090, 4254, 4490

Offset: 0

Author

Aldo González Lorenzo, Oct 10 2011

Keywords

• nonn

Comments

It is also the number of 2 X 2 integer matrices with elements from {1,...,n} whose determinant is -2.

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..10000

Programs

Mathematica

Table[cnt = 0; Do[If[a*d-b*c == 2, cnt++], {a, n}, {b, n}, {c, n}, {d, n}]; cnt, {n, 50}] (* T. D. Noe, Oct 11 2011 *)

Formula

a(n) = A209973(n) - 4*n - 2 for n >= 2. - Chai Wah Wu, Nov 28 2016

Extensions

a(0) added by Chai Wah Wu, Nov 27 2016