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A125586
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a(n) = 2^(2n-1) - (n+2)*3^(n-2).
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2
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1, 4, 17, 74, 323, 1400, 6005, 25478, 107015, 445556, 1841273, 7561922, 30897227, 125714672, 509767421, 2061390206, 8317305359, 33498803948, 134727010049, 541232563130, 2172291241811, 8712410196584, 34922863258757, 139921580805494, 560408087592983
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OFFSET
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1,2
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COMMENTS
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Number of n X n nonsingular real matrices with entries {0,1} in which the top left n-1 X n-1 submatrix is the identity matrix. See A125587 for proof.
The number of singular matrices is given by A006234.
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LINKS
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FORMULA
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G.f.: -x*(10*x^2-6*x+1) / ((3*x-1)^2*(4*x-1)). - Colin Barker, Feb 26 2014
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EXAMPLE
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a(2) = 4:
10 10 11 11
01 11 01 10
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MAPLE
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MATHEMATICA
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LinearRecurrence[{10, -33, 36}, {1, 4, 17}, 50] (* Harvey P. Dale, Sep 15 2019 *)
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PROG
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(PARI) Vec(-x*(10*x^2-6*x+1)/((3*x-1)^2*(4*x-1)) + O(x^100)) \\ Colin Barker, Feb 26 2014
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CROSSREFS
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KEYWORD
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nonn,easy,changed
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AUTHOR
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STATUS
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approved
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