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A047262
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Numbers that are congruent to {0, 2, 4, 5} mod 6.
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3
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0, 2, 4, 5, 6, 8, 10, 11, 12, 14, 16, 17, 18, 20, 22, 23, 24, 26, 28, 29, 30, 32, 34, 35, 36, 38, 40, 41, 42, 44, 46, 47, 48, 50, 52, 53, 54, 56, 58, 59, 60, 62, 64, 65, 66, 68, 70, 71, 72, 74, 76, 77, 78, 80, 82, 83, 84, 86, 88, 89, 90, 92, 94, 95, 96, 98
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: x^2*(2+x^2) / ( (1+x^2)*(1-x)^2 ).
a(n) = 3*n/2 - 1 - sin(Pi*n/2)/2. (End)
a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n > 4.
a(n) = (6*n - 4 - i^(1-n) + i^(1+n))/4, where i = sqrt(-1).
a(n) = (6*n - 4 - (1 - (-1)^n)*(-1)^(n*(n-1)/2))/4.
a(n) = a(n-4) + 6, a(1)=0, a(2)=2, a(3)=4, a(4)=5, for n > 4. (End)
Sum_{n>=2} (-1)^n/a(n) = log(3)/4 + log(2)/3 - sqrt(3)*Pi/36. - Amiram Eldar, Dec 17 2021
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MAPLE
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MATHEMATICA
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Select[Range[0, 100], MemberQ[{0, 2, 4, 5}, Mod[#, 6]]&] (* or *) LinearRecurrence[{2, -2, 2, -1}, {0, 2, 4, 5}, 70] (* Harvey P. Dale, Dec 09 2015 *)
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PROG
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(Magma) [n : n in [0..100] | n mod 6 in [0, 2, 4, 5]]; // Wesley Ivan Hurt, May 21 2016
(PARI) my(x='x+O('x^70)); concat([0], Vec(x^2*(2+x^2)/((1+x^2)*(1-x)^2))) \\ G. C. Greubel, Feb 16 2019
(Sage) a=(x^2*(2+x^2)/((1+x^2)*(1-x)^2)).series(x, 72).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Feb 16 2019
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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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