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A123920
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Number of numbers congruent to 2 or 4 mod 6 between n and 2n inclusive.
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1
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1, 2, 1, 2, 2, 2, 3, 4, 3, 4, 4, 4, 5, 6, 5, 6, 6, 6, 7, 8, 7, 8, 8, 8, 9, 10, 9, 10, 10, 10, 11, 12, 11, 12, 12, 12, 13, 14, 13, 14, 14, 14, 15, 16, 15, 16, 16, 16, 17, 18, 17, 18, 18, 18, 19, 20, 19, 20, 20, 20, 21, 22, 21, 22, 22, 22, 23, 24, 23, 24, 24, 24, 25, 26, 25, 26, 26, 26
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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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Odd a(n) = (2k - 1) for n = {6k - 5, 6k - 3), where k = 1,2,3,... Even a(n) = 2k for n = {6k - 4, 6k - 2, 6k - 1, 6k}, where k = 1,2,3,... - Alexander Adamchuk, Nov 08 2006
G.f.: x*(1+x-x^2+x^3)/((1-x)*(1-x^6)). - G. C. Greubel, Aug 07 2019
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MAPLE
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seq(coeff(series(x*(1+x-x^2+x^3)/((1-x)*(1-x^6)), x, n+1), x, n), n = 1..80); # G. C. Greubel, Aug 07 2019
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MATHEMATICA
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Table[Count[Range[n, 2n], _?(MemberQ[{2, 4}, Mod[#, 6]]&)], {n, 80}] (* Harvey P. Dale, Mar 25 2019 *)
LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {1, 2, 1, 2, 2, 2, 3}, 80] (* G. C. Greubel, Aug 07 2019 *)
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PROG
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(PARI) my(x='x+O('x^80)); Vec(x*(1+x-x^2+x^3)/((1-x)*(1-x^6))) \\ G. C. Greubel, Aug 07 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( x*(1+x-x^2+x^3)/((1-x)*(1-x^6)) )); // G. C. Greubel, Aug 07 2019
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x*(1+x-x^2+x^3)/((1-x)*(1-x^6)) ).list()
(GAP) a:=[1, 2, 1, 2, 2, 2, 3];; for n in [8..80] do a[n]:=a[n-1]+a[n-6]-a[n-7]; od; a; # G. C. Greubel, Aug 07 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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