A047593 Numbers that are congruent to {2, 3, 4, 5, 6, 7} mod 8.

2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 18, 19, 20, 21, 22, 23, 26, 27, 28, 29, 30, 31, 34, 35, 36, 37, 38, 39, 42, 43, 44, 45, 46, 47, 50, 51, 52, 53, 54, 55, 58, 59, 60, 61, 62, 63, 66, 67, 68, 69, 70, 71, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1).

Formula

G.f.: x*(2+x+x^2+x^3+x^4+x^5+x^6) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2 ). - R. J. Mathar, Jul 10 2015

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-3-3*cos(n*Pi)-4*sqrt(3)*cos((1+4*n)*Pi/6)-12*sin((1-2*n)*Pi/6))/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-6. (End)

Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(2)+1)*Pi/16 + sqrt(2)*log(sqrt(2)+2)/8 - (sqrt(2)+8)*log(2)/16. - Amiram Eldar, Dec 28 2021

Maple

A047593:=n->(24*n-3-3*cos(n*Pi)-4*sqrt(3)*cos((1+4*n)*Pi/6)-12*sin((1-2*n)*Pi/6))/18: seq(A047593(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016

Mathematica

Select[Range[100], MemberQ[{2, 3, 4, 5, 6, 7}, Mod[#, 8]]&] (* Vincenzo Librandi, Jan 06 2013 *)

Prog

(Magma) [n: n in [1..80] | n mod 8 in [2..7]]; // Vincenzo Librandi, Jan 06 2013

Crossrefs

Cf. A047564, A047572.

Sequence in context: A143719 A078779 A351958 * A181046 A032879 A032846

Adjacent sequences: A047590 A047591 A047592 * A047594 A047595 A047596

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved