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A047572
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Numbers that are congruent to {1, 2, 4, 5, 6, 7} mod 8.
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3
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1, 2, 4, 5, 6, 7, 9, 10, 12, 13, 14, 15, 17, 18, 20, 21, 22, 23, 25, 26, 28, 29, 30, 31, 33, 34, 36, 37, 38, 39, 41, 42, 44, 45, 46, 47, 49, 50, 52, 53, 54, 55, 57, 58, 60, 61, 62, 63, 65, 66, 68, 69, 70, 71, 73, 74, 76, 77, 78, 79, 81, 82, 84, 85, 86, 87
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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*(1+x+2*x^2+x^3+x^4+x^5+x^6) / ((x-1)^2*(1+x+x^2+x^3+x^4+x^5)).
a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.
a(n) = (24*n-9-3*cos(n*Pi)-6*cos(n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/18.
a(6k) = 8k-1, a(6k-1) = 8k-2, a(6k-2) = 8k-3, a(6k-3) = 8k-4, a(6k-4) = 8k-6, a(6k-5) = 8k-7. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = (3*sqrt(2)-1)*Pi/16 + sqrt(2)*log(sqrt(2)+2)/8 - (sqrt(2)+4)*log(2)/16. - Amiram Eldar, Dec 28 2021
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MAPLE
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MATHEMATICA
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Select[Range[0, 100], MemberQ[{1, 2, 4, 5, 6, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 16 2016 *)
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PROG
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(Magma) [n : n in [0..100] | n mod 8 in [1, 2, 4, 5, 6, 7]]; // Wesley Ivan Hurt, Jun 16 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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