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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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A098751 A143190 A009771 * A079273 A271991 A048469
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

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Last modified March 3 03:04 EST 2024. Contains 370499 sequences. (Running on oeis4.)