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A047347
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Numbers that are congruent to {0, 1, 4} mod 7.
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2
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0, 1, 4, 7, 8, 11, 14, 15, 18, 21, 22, 25, 28, 29, 32, 35, 36, 39, 42, 43, 46, 49, 50, 53, 56, 57, 60, 63, 64, 67, 70, 71, 74, 77, 78, 81, 84, 85, 88, 91, 92, 95, 98, 99, 102, 105, 106, 109, 112, 113, 116, 119, 120, 123, 126, 127, 130, 133, 134, 137, 140, 141
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OFFSET
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1,3
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LINKS
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FORMULA
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G.f.: x^2*(1+3*x+3*x^2)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Oct 08 2011
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
a(n) = 7*n/3-3+4*sin(2*n*Pi/3)/(3*sqrt(3)).
a(3k) = 7k-3, a(3k-1) = 7k-6, a(3k-2) = 7k-7. (End)
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MAPLE
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MATHEMATICA
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Select[Range[0, 200], MemberQ[{0, 1, 4}, Mod[#, 7]]&] (* or *) LinearRecurrence[{1, 0, 1, -1}, {0, 1, 4, 7}, 100] (* Harvey P. Dale, Dec 05 2012 *)
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PROG
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(Magma) [n : n in [0..150] | n mod 7 in [0, 1, 4]]; // Wesley Ivan Hurt, Jun 10 2016
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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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STATUS
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approved
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