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A047517
Numbers that are congruent to {0, 1, 3, 4, 6, 7} mod 8.
4
0, 1, 3, 4, 6, 7, 8, 9, 11, 12, 14, 15, 16, 17, 19, 20, 22, 23, 24, 25, 27, 28, 30, 31, 32, 33, 35, 36, 38, 39, 40, 41, 43, 44, 46, 47, 48, 49, 51, 52, 54, 55, 56, 57, 59, 60, 62, 63, 64, 65, 67, 68, 70, 71, 72, 73, 75, 76, 78, 79, 80, 81, 83, 84, 86, 87, 88, 89
OFFSET
1,3
FORMULA
From Chai Wah Wu, May 30 2016: (Start)
a(n) = a(n-1) + a(n-6) - a(n-7), for n > 7.
G.f.: x^2*(x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^7 - x^6 - x + 1). (End)
From Wesley Ivan Hurt, Jun 16 2016: (Start)
a(n) = (24*n-21-3*cos(n*Pi)+2*sqrt(3)*cos((1+4*n)*Pi/6)+6*sin((1-2*n)*Pi/6))/18.
a(6k) = 8k-1, a(6k-1) = 8k-2, a(6k-2) = 8k-4, a(6k-3) = 8k-5, a(6k-4) = 8k-7, a(6k-5) = 8k-8. (End)
Sum_{n>=2} (-1)^n/a(n) = (2-sqrt(2))*Pi/16 + (6-3*sqrt(2))*log(2)/16 + 3*sqrt(2)*log(sqrt(2)+2)/8. - Amiram Eldar, Dec 27 2021
MAPLE
A047424:=n->(24*n-21-3*cos(n*Pi)+2*sqrt(3)*cos((1+4*n)*Pi/6)+6*sin((1-2*n)* Pi/6))/18: seq(A047424(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016
MATHEMATICA
LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 1, 3, 4, 6, 7, 8}, 50] (* G. C. Greubel, May 30 2016 *)
Select[Range[0, 200], MemberQ[{0, 1, 3, 4, 6, 7}, Mod[#, 8]] &] (* Vincenzo Librandi, May 30 2016 *)
PROG
(Magma) [n: n in [0..110] | n mod 8 in [0, 1, 3, 4, 6, 7]]; // Vincenzo Librandi, May 30 2016
(PARI) my(x='x+O('x^50)); concat([0], Vec(x^2*(x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^7 - x^6 - x + 1))) \\ G. C. Greubel, Oct 29 2017
CROSSREFS
Sequence in context: A182835 A058654 A188435 * A206587 A192450 A039064
KEYWORD
nonn,easy
STATUS
approved