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

0,3

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

Formula

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

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 *)

Crossrefs

Sequence in context: A066286 A324541 A351875 * A373515 A288815 A277200

Adjacent sequences: A197165 A197166 A197167 * A197169 A197170 A197171

Keyword

nonn

Author

Aldo González Lorenzo, Oct 10 2011

Extensions

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

Status

approved