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A209993
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Number of 2 X 2 matrices with all elements in {0,1,...,n} and determinant in {-1,0,1}.
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1
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1, 16, 45, 94, 159, 248, 349, 478, 623, 792, 973, 1182, 1423, 1672, 1933, 2238, 2559, 2888, 3261, 3630, 4063, 4504, 4925, 5374, 5935, 6456, 6957, 7534, 8159, 8728, 9453, 10062, 10767, 11480, 12141, 12942, 13855, 14584, 15325, 16174, 17183
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OFFSET
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0,2
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COMMENTS
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See A210000 for a guide to related sequences.
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LINKS
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FORMULA
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MAPLE
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pillai:= proc(n) local i; add(igcd(i, n), i=1..n) end proc:
T:= 16: R:= 1, 16:
for n from 2 to 50 do
v:= 1 + 4*n + 8*numtheory:-phi(n) + 4*pillai(n);
T:= T + v;
R:= R, T;
od:
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MATHEMATICA
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a = 1; b = n; z1 = 40;
t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
c[n_, k_] := c[n, k] = Count[t[n], k]
c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, 0, 1}]
Table[c1[n, 1], {n, 0, z1}] (* A209992 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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