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A068197
Number of squares (of another matrix) in M_2(n) - the ring of 2 X 2 matrices over Z_n.
3
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
1,2
COMMENTS
a(n) is multiplicative. This is the 2-dimensional analog of A000224.
LINKS
PROG
(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
(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
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Sharon Sela (sharonsela(AT)hotmail.com), Mar 23 2002
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
STATUS
approved