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A209982
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Number of 2 X 2 matrices having all elements in {-n,...,n} and determinant 1.
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4
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0, 20, 52, 116, 180, 308, 372, 564, 692, 884, 1012, 1332, 1460, 1844, 2036, 2292, 2548, 3060, 3252, 3828, 4084, 4468, 4788, 5492, 5748, 6388, 6772, 7348, 7732, 8628, 8884, 9844, 10356, 10996, 11508, 12276, 12660, 13812, 14388, 15156
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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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Andrew Howroyd, Table of n, a(n) for n = 0..1000
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FORMULA
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From Andrew Howroyd, May 05 2020: (Start)
a(n) = 8*A196227(n) + 4*(4*n + 1) = 8*A171503(n) - 4 for n > 0.
a(n) = -12 + 32*Sum_{k=1..n} phi(k) for n > 0. (End)
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MATHEMATICA
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(See the Mathematica section at A209981.)
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PROG
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(PARI) a(n)=if(n<1, 0, 32*sum(k=1, n, eulerphi(k)) - 12) \\ Andrew Howroyd, May 05 2020
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CROSSREFS
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Cf. A171503, A196227, A210000.
Sequence in context: A350115 A211143 A183047 * A205220 A188250 A329627
Adjacent sequences: A209979 A209980 A209981 * A209983 A209984 A209985
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling, Mar 17 2012
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STATUS
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approved
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