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A029739
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Numbers that are congruent to {1, 3, 4} mod 6.
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3
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1, 3, 4, 7, 9, 10, 13, 15, 16, 19, 21, 22, 25, 27, 28, 31, 33, 34, 37, 39, 40, 43, 45, 46, 49, 51, 52, 55, 57, 58, 61, 63, 64, 67, 69, 70, 73, 75, 76, 79, 81, 82, 85, 87, 88, 91, 93, 94, 97, 99, 100, 103, 105, 106, 109, 111, 112, 115, 117, 118, 121, 123, 124
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: x*(2*x+1)*(x^2+1)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Aug 24 2011
a(n) = a(n-1) + a(n-3) - a(n-4) for n > 4.
a(n) = 2*(3*n - 2 - cos(2*n*Pi/3))/3.
a(3k) = 6k-2, a(3k-1) = 6k-3, a(3k-2) = 6k-5. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = (3+2*sqrt(3))*Pi/36 + log(2+sqrt(3))/(2*sqrt(3)) - log(2)/6. - Amiram Eldar, Dec 16 2021
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MAPLE
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MATHEMATICA
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Select[Range[0, 202], MemberQ[{1, 3, 4}, Mod[#, 6]] &] (* and *) Join[{1}, Accumulate[Total /@ CellularAutomaton[65, {1, 1, 0, 0, 1, 0}, 100]]] (* Vladimir Joseph Stephan Orlovsky, Feb 11 2012 *)
LinearRecurrence[{1, 0, 1, -1}, {1, 3, 4, 7}, 80] (* Harvey P. Dale, Aug 21 2021 *)
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PROG
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(Magma) [n : n in [0..150] | n mod 6 in {1, 3, 4}]; // Vincenzo Librandi, Dec 29 2010
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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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