A047450 Numbers that are congruent to {0, 1, 2, 3, 5, 6} mod 8.

0, 1, 2, 3, 5, 6, 8, 9, 10, 11, 13, 14, 16, 17, 18, 19, 21, 22, 24, 25, 26, 27, 29, 30, 32, 33, 34, 35, 37, 38, 40, 41, 42, 43, 45, 46, 48, 49, 50, 51, 53, 54, 56, 57, 58, 59, 61, 62, 64, 65, 66, 67, 69, 70, 72, 73, 74, 75, 77, 78, 80, 81, 82, 83, 85, 86, 88

Offset

1,3

Links

Table of n, a(n) for n=1..67.

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

Formula

G.f.: x^2*(1+x+x^2+2*x^3+x^4+2*x^5) / ((1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2). - R. J. Mathar, Dec 07 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-33-3*cos(n*Pi)-2*sqrt(3)*cos((1-4*n)*Pi/6)+6*sin((1+2*n) *Pi/6))/18.

a(6k) = 8k-2, a(6k-1) = 8k-3, a(6k-2) = 8k-5, a(6k-3) = 8k-6, a(6k-4) = 8k-7, a(6k-5) = 8k-8. (End)

Sum_{n>=2} (-1)^n/a(n) = 3*(sqrt(2)-1)*Pi/16 + (8-sqrt(2))*log(2)/16 + sqrt(2)*log(sqrt(2)+2)/8. - Amiram Eldar, Dec 26 2021

Maple

A047450:=n->(24*n-33-3*cos(n*Pi)-2*sqrt(3)*cos((1-4*n)*Pi/6)+6*sin((1+2*n) *Pi/6))/18: seq(A047450(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016

Mathematica

Select[Range[0, 100], MemberQ[{0, 1, 2, 3, 5, 6}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 16 2016 *)

Prog

(Magma) [n : n in [0..100] | n mod 8 in [0, 1, 2, 3, 5, 6]]; // Wesley Ivan Hurt, Jun 16 2016

Crossrefs

Cf. A047420, A047602.

Sequence in context: A184861 A183572 A285962 * A039073 A026359 A367917

Adjacent sequences: A047447 A047448 A047449 * A047451 A047452 A047453

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved