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A047310
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Numbers that are congruent to {0, 1, 3, 4, 5, 6} mod 7.
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1
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0, 1, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78
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OFFSET
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1,3
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COMMENTS
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LINKS
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FORMULA
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G.f.: x^2*(1+2*x+x^2+x^3+x^4+x^5) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2 ). - R. J. Mathar, Oct 25 2011
a(n) = a(n-1)+a(n-6)-a(n-7) for n>7.
a(n) = n + floor((n-3)/6). (End)
a(n) = (42*n-33-3*cos(n*Pi)+4*sqrt(3)*cos((1-4*n)*Pi/6)-12*sin((1+2*n)*Pi/6))/36.
a(6k) = 7k-1, a(6k-1) = 7k-2, a(6k-2) = 7k-3, a(6k-3) = 7k-4, a(6k-4) = 7k-6, a(6k-5) = 7k-7. (End)
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MAPLE
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MATHEMATICA
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LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 1, 3, 4, 5, 6, 7}, 70] (* Vincenzo Librandi, Sep 10 2015 *)
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PROG
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(Magma) [n: n in [0..100] | n mod 7 in [0, 1, 3, 4, 5, 6]]; // Vincenzo Librandi, Sep 10 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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