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