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A047318
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Numbers that are congruent to {0, 1, 2, 4, 5, 6} mod 7.
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2
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0, 1, 2, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 81, 82, 83
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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+x+2*x^2+x^3+x^4+x^5) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2 ). - R. J. Mathar, Dec 03 2011
a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.
a(n) = n + floor((n-4)/6). (End)
a(n) = (42*n-39+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-5, a(6k-4) = 7k-6, a(6k-5) = 7k-7. (End)
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MAPLE
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for n from 0 to 200 do if n mod 7 <> 3 then printf(`%d, `, n) fi: od:
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MATHEMATICA
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LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 1, 2, 4, 5, 6, 7}, 100] (* Vincenzo Librandi, Sep 11 2015 *)
DeleteCases[Range[0, 100], _?(Mod[#, 7]==3&)] (* Harvey P. Dale, May 07 2016 *)
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PROG
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(Magma) [n : n in [0..140] | n mod 7 in [0, 1, 2, 4, 5, 6]]; // Vincenzo Librandi, Sep 11 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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