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A047519
Numbers that are congruent to {1, 2, 3, 4, 6, 7} mod 8.
4
1, 2, 3, 4, 6, 7, 9, 10, 11, 12, 14, 15, 17, 18, 19, 20, 22, 23, 25, 26, 27, 28, 30, 31, 33, 34, 35, 36, 38, 39, 41, 42, 43, 44, 46, 47, 49, 50, 51, 52, 54, 55, 57, 58, 59, 60, 62, 63, 65, 66, 67, 68, 70, 71, 73, 74, 75, 76, 78, 79, 81, 82, 83, 84, 86, 87
OFFSET
1,2
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*(x^6 + x^5 + 2*x^4 + x^3 + x^2 + x + 1)/(x^7 - x^6 - x + 1). (End)
From Wesley Ivan Hurt, Jun 16 2016: (Start)
a(n) = (24*n-15-3*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-6, a(6k-5) = 8k-7. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = (3*sqrt(2)-1)*Pi/16 + log(2)/4 + sqrt(2)*log(3-2*sqrt(2))/16. - Amiram Eldar, Dec 28 2021
MAPLE
A047519:=n->(24*n-15-3*cos(n*Pi)-2*sqrt(3)*cos((1-4*n)*Pi/6)+6*sin((1+2*n)
*Pi/6))/18: seq(A047519(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016
MATHEMATICA
LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {1, 2, 3, 4, 6, 7, 9}, 50] (* G. C. Greubel, May 30 2016 *)
PROG
(Magma) [n : n in [0..100] | n mod 8 in [1, 2, 3, 4, 6, 7]]; // Wesley Ivan Hurt, Jun 16 2016
CROSSREFS
Sequence in context: A285974 A227194 A039054 * A070118 A070124 A059097
KEYWORD
nonn,easy
STATUS
approved