A068197 Number of squares (of another matrix) in M_2(n) - the ring of 2 X 2 matrices over Z_n.
1, 10, 29, 48, 223, 290, 865, 344, 1587, 2230, 5341, 1392, 10459, 8650, 6467, 3182, 30745, 15870, 48061, 10704, 25085, 53410, 103489, 9976, 108035, 104590, 118179, 41520, 262291, 64670, 342721, 41736, 154889, 307450, 192895, 76176, 696655, 480610, 303311, 76712, 1051261, 250850, 1272349, 256368, 353901
Offset: 1
Links
- Giovanni Resta, Table of n, a(n) for n = 1..210
Programs
-
PARI
a(n)={my(M=Map()); for(a=0, n-1, for(b=0, n-1, for(c=0, n-1, for(d=0, n-1, mapput(M, lift(Mod([a, b; c, d], n)^2), 1))))); #M} \\ Andrew Howroyd, Aug 06 2018 -
Sage
def A68197(n): S = set() L = list(range(n)) for a, b, c, d in cartesian_product([L, L, L, L]): M = Matrix([[a, b], [c, d]]) N = tuple(x % n for x in (M * M).list()) if N not in S: S.add(N) print(n, len(S)) # Manfred Scheucher, Jun 12 2015
Extensions
More terms from Manfred Scheucher, Jun 12 2015
a(45) corrected by Giovanni Resta, Jun 12 2015
a(1) added by Andrew Howroyd, Aug 06 2018
Comments