A047587 Numbers that are congruent to {0, 2, 3, 5, 6, 7} mod 8.

0, 2, 3, 5, 6, 7, 8, 10, 11, 13, 14, 15, 16, 18, 19, 21, 22, 23, 24, 26, 27, 29, 30, 31, 32, 34, 35, 37, 38, 39, 40, 42, 43, 45, 46, 47, 48, 50, 51, 53, 54, 55, 56, 58, 59, 61, 62, 63, 64, 66, 67, 69, 70, 71, 72, 74, 75, 77, 78, 79, 80, 82, 83, 85, 86, 87

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

From Wesley Ivan Hurt, Jun 16 2016: (Start)

G.f.: x^2*(2+x+2*x^2+x^3+x^4+x^5)/((x-1)^2*(1+x+x^2+x^3+x^4+x^5)).

a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.

a(n) = (24*n-15+3*cos(n*Pi)-2*sqrt(3)*cos((1-4*n)*Pi/6)-6*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-5, a(6k-4) = 8k-6, a(6k-5) = 8k-8. (End)

Sum_{n>=2} (-1)^n/a(n) = (8-sqrt(2))*log(2)/16 + sqrt(2)*log(sqrt(2)+2)/8 - 3*(sqrt(2)-1)*Pi/16. - Amiram Eldar, Dec 27 2021

Maple

A047587:=n->(24*n-15+3*cos(n*Pi)-2*sqrt(3)*cos((1-4*n)*Pi/6)-6*sin((1+2*n)*Pi/6))/18: seq(A047587(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016

Mathematica

Select[Range[0, 150], MemberQ[{0, 2, 3, 5, 6, 7}, Mod[#, 8]]&] (* Harvey P. Dale, Oct 04 2011 *)

Prog

(Magma) [n : n in [0..100] | n mod 8 in [0, 2, 3, 5, 6, 7]]; // Wesley Ivan Hurt, Jun 16 2016

Crossrefs

Cf. A047503, A047571.

Sequence in context: A336590 A000452 A307295 * A285420 A028737 A371731

Adjacent sequences: A047584 A047585 A047586 * A047588 A047589 A047590

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved