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A047602
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Numbers that are congruent to {0, 1, 2, 3, 4, 5} mod 8.
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5
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0, 1, 2, 3, 4, 5, 8, 9, 10, 11, 12, 13, 16, 17, 18, 19, 20, 21, 24, 25, 26, 27, 28, 29, 32, 33, 34, 35, 36, 37, 40, 41, 42, 43, 44, 45, 48, 49, 50, 51, 52, 53, 56, 57, 58, 59, 60, 61, 64, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 77, 80, 81, 82, 83, 84, 85, 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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a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.
G.f.: x^2*(3*x^5 + x^4 + x^3 + x^2 + x + 1)/(x^7 - x^6 - x + 1). (End)
a(n) = (24*n-39-3*cos(n*Pi)-4*sqrt(3)*cos((4*n+1)*Pi/6)-12*sin((1-2*n)*Pi/6))/18.
a(6k) = 8k-3, a(6k-1) = 8k-4, a(6k-2) = 8k-5, a(6k-3) = 8k-6, a(6k-4) = 8k-7, a(6k-5) = 8k-8. (End)
Sum_{n>=2} (-1)^n/a(n) = sqrt(2)*Pi/16 + 7*log(2)/8 + sqrt(2)*log(3-2*sqrt(2))/16. - Amiram Eldar, Dec 26 2021
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MAPLE
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MATHEMATICA
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Table[Floor[(8/7) Floor[7 (n - 1) / 6]], {n, 80}] (* Vincenzo Librandi, May 04 2016 *)
LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 1, 2, 3, 4, 5, 8}, 50] (* G. C. Greubel, May 29 2016 *)
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PROG
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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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