A047422 Numbers that are congruent to {1, 2, 3, 4, 5, 6} mod 8.

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

Offset

1,2

Links

Table of n, a(n) for n=1..66.

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

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

Cf. A047504, A047519.

Sequence in context: A037475 A354047 A031487 * A340152 A160532 A047305

Adjacent sequences: A047419 A047420 A047421 * A047423 A047424 A047425

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved