A047571 Numbers that are congruent to {0, 2, 4, 5, 6, 7} mod 8.

0, 2, 4, 5, 6, 7, 8, 10, 12, 13, 14, 15, 16, 18, 20, 21, 22, 23, 24, 26, 28, 29, 30, 31, 32, 34, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 50, 52, 53, 54, 55, 56, 58, 60, 61, 62, 63, 64, 66, 68, 69, 70, 71, 72, 74, 76, 77, 78, 79, 80, 82, 84, 85, 86, 87, 88, 90

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-2,2,-1).

Formula

From Chai Wah Wu, May 30 2016: (Start)

a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-2*a(n-4)+2*a(n-5)-a(n-6) for n>6.

G.f.: x^2*(x^4 + x^2 + 2)/((x - 1)^2*(x^2 - x + 1)*(x^2 + x + 1)). (End)

a(n) = (8*n - 2*sqrt(3)*sin(Pi*(n+1)/3) + 2*sin(2*Pi*(n+1)/3)/sqrt(3) - 4)/6. - Ilya Gutkovskiy, May 30 2016

a(6k) = 8k-1, a(6k-1) = 8k-2, a(6k-2) = 8k-3, a(6k-3) = 8k-4, a(6k-4) = 8k-6, a(6k-5) = 8k-8. - Wesley Ivan Hurt, Jun 16 2016

Sum_{n>=2} (-1)^n/a(n) = 3*log(2)/4 - (sqrt(2)-1)*Pi/8. - Amiram Eldar, Dec 27 2021

Maple

A047571:=n->(8*n-2*sqrt(3)*sin(Pi*(n+1)/3)+2*sin(2*Pi*(n+1)/3)/sqrt(3)-4)/6: seq(A047571(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016

Mathematica

LinearRecurrence[{2, -2, 2, -2, 2, -1}, {0, 2, 4, 5, 6, 7} , 50] (* G. C. Greubel, May 30 2016 *)

Prog

(Magma) [n: n in [0..200] | n mod 8 in [0, 2, 4, 5, 6, 7]]; // Vincenzo Librandi, May 30 2016

Crossrefs

Cf. A047587, A047563.

Sequence in context: A260375 A361144 A188160 * A190237 A190225 A276706

Adjacent sequences: A047568 A047569 A047570 * A047572 A047573 A047574

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved