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A047563
Numbers that are congruent to {0, 3, 4, 5, 6, 7} mod 8.
2
0, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14, 15, 16, 19, 20, 21, 22, 23, 24, 27, 28, 29, 30, 31, 32, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 59, 60, 61, 62, 63, 64, 67, 68, 69, 70, 71, 72, 75, 76, 77, 78, 79, 80, 83, 84, 85, 86, 87
OFFSET
1,2
FORMULA
From Chai Wah Wu, May 29 2016: (Start)
a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.
G.f.: x^2*(x^5 + x^4 + x^3 + x^2 + x + 3)/(x^7 - x^6 - x + 1). (End)
From Wesley Ivan Hurt, Jun 16 2016: (Start)
a(n) = (24*n-9+3*cos(n*Pi)-12*cos(n*Pi/3)-4*sqrt(3)*sin(2*n*Pi/3))/18.
a(6k) = 8k-1, a(6k-1) = 8k-2, a(6k-2) = 8k-3, a(6k-3) = 8k-4, a(6k-4) = 8k-5, a(6k-5) = 8k-8. (End)
Sum_{n>=2} (-1)^n/a(n) = 7*log(2)/8 + sqrt(2)*log(3-2*sqrt(2))/16 - sqrt(2)*Pi/16. - Amiram Eldar, Dec 27 2021
MAPLE
A047563:=n->(24*n-9+3*cos(n*Pi)-12*cos(n*Pi/3)-4*sqrt(3)*sin(2*n*Pi/3))/18: seq(A047563(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016
MATHEMATICA
LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 3, 4, 5, 6, 7, 8}, 50] (* G. C. Greubel, May 29 2016 *)
PROG
(Magma) [n : n in [0..100] | n mod 8 in [0] cat [3..7]]; // Wesley Ivan Hurt, May 29 2016
CROSSREFS
Cf. A047571.
Sequence in context: A273664 A364099 A332416 * A261604 A120561 A051016
KEYWORD
nonn,easy
STATUS
approved