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A047498
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Numbers that are congruent to {0, 1, 2, 4, 5, 7} mod 8.
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3
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0, 1, 2, 4, 5, 7, 8, 9, 10, 12, 13, 15, 16, 17, 18, 20, 21, 23, 24, 25, 26, 28, 29, 31, 32, 33, 34, 36, 37, 39, 40, 41, 42, 44, 45, 47, 48, 49, 50, 52, 53, 55, 56, 57, 58, 60, 61, 63, 64, 65, 66, 68, 69, 71, 72, 73, 74, 76, 77, 79, 80, 81, 82, 84, 85, 87, 88
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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*(x^5+2*x^4+x^3+2*x^2+x+1)/((x-1)^2*(x+1)*(x^2-x+1)*(x^2+x+1)). - Colin Barker, Jun 22 2012
a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.
a(n) = (24*n-27+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-3, a(6k-2) = 8k-4, a(6k-3) = 8k-6, a(6k-4) = 8k-7, a(6k-5) = 8k-8. (End)
Sum_{n>=2} (-1)^n/a(n) = (6-3*sqrt(2))*log(2)/16 + 3*sqrt(2)*log(sqrt(2)+2)/8 - (2-sqrt(2))*Pi/16. - Amiram Eldar, Dec 27 2021
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MAPLE
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MATHEMATICA
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Select[Range[0, 100], MemberQ[{0, 1, 2, 4, 5, 7}, Mod[#, 8]]&] (* or *) LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 1, 2, 4, 5, 7, 8}, 100] (* Harvey P. Dale, Jul 23 2015 *)
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PROG
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(Magma) [n : n in [0..100] | n mod 8 in [0, 1, 2, 4, 5, 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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