A047498 Numbers that are congruent to {0, 1, 2, 4, 5, 7} mod 8.

0, 1, 2, 4, 5, 7, 8, 9, 10, 12, 13, 15, 16, 17, 18, 20, 21, 23, 24, 25, 26, 28, 29, 31, 32, 33, 34, 36, 37, 39, 40, 41, 42, 44, 45, 47, 48, 49, 50, 52, 53, 55, 56, 57, 58, 60, 61, 63, 64, 65, 66, 68, 69, 71, 72, 73, 74, 76, 77, 79, 80, 81, 82, 84, 85, 87, 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*(x^5+2*x^4+x^3+2*x^2+x+1)/((x-1)^2*(x+1)*(x^2-x+1)*(x^2+x+1)). - Colin Barker, Jun 22 2012

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-27+3*cos(n*Pi)+6*cos(n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/18.

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

Sum_{n>=2} (-1)^n/a(n) = (6-3*sqrt(2))*log(2)/16 + 3*sqrt(2)*log(sqrt(2)+2)/8 - (2-sqrt(2))*Pi/16. - Amiram Eldar, Dec 27 2021

Maple

A047498:=n->(24*n-27+3*cos(n*Pi)+6*cos(n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/18: seq(A047498(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016

Mathematica

Select[Range[0, 100], MemberQ[{0, 1, 2, 4, 5, 7}, Mod[#, 8]]&] (* or *) LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 1, 2, 4, 5, 7, 8}, 100] (* Harvey P. Dale, Jul 23 2015 *)

Prog

(Magma) [n : n in [0..100] | n mod 8 in [0, 1, 2, 4, 5, 7]]; // Wesley Ivan Hurt, Jun 16 2016

Crossrefs

Cf. A047513, A047581.

Sequence in context: A183573 A187895 A079726 * A026367 A039069 A285423

Adjacent sequences: A047495 A047496 A047497 * A047499 A047500 A047501

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved