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A047422 Numbers that are congruent to {1, 2, 3, 4, 5, 6} mod 8. 4
1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 25, 26, 27, 28, 29, 30, 33, 34, 35, 36, 37, 38, 41, 42, 43, 44, 45, 46, 49, 50, 51, 52, 53, 54, 57, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 73, 74, 75, 76, 77, 78, 81, 82, 83, 84, 85, 86 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
G.f.: x*(1+x+x^2+x^3+x^4+x^5+2*x^6) / ((1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2). - R. J. Mathar, Dec 05 2011
From Wesley Ivan Hurt, Jun 16 2016: (Start)
a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.
a(n) = (24*n-21-3*cos(n*Pi)-4*sqrt(3)*cos((1+4*n)*Pi/6)-12*sin((1-2*n)*Pi/6))/18.
a(6k) = 8k-2, a(6k-1) = 8k-3, a(6k-2) = 8k-4, a(6k-3) = 8k-5, a(6k-4) = 8k-6, a(6k-5) = 8k-7. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(2)+1)*Pi/16 + log(2)/2 + sqrt(2)*log(3-2*sqrt(2))/16. - Amiram Eldar, Dec 28 2021
MAPLE
A047422:=n->(24*n-21-3*cos(n*Pi)-4*sqrt(3)*cos((1+4*n)*Pi/6)-12*sin((1-2*n)*Pi/6))/18: seq(A047422(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016
MATHEMATICA
Select[Range[0, 100], MemberQ[{1, 2, 3, 4, 5, 6}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 16 2016 *)
PROG
(Magma) [n : n in [0..100] | n mod 8 in [1..6]]; // Wesley Ivan Hurt, Jun 16 2016
CROSSREFS
Sequence in context: A037475 A354047 A031487 * A340152 A160532 A047305
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified May 26 16:22 EDT 2024. Contains 372840 sequences. (Running on oeis4.)