A047519 Numbers that are congruent to {1, 2, 3, 4, 6, 7} mod 8.

1, 2, 3, 4, 6, 7, 9, 10, 11, 12, 14, 15, 17, 18, 19, 20, 22, 23, 25, 26, 27, 28, 30, 31, 33, 34, 35, 36, 38, 39, 41, 42, 43, 44, 46, 47, 49, 50, 51, 52, 54, 55, 57, 58, 59, 60, 62, 63, 65, 66, 67, 68, 70, 71, 73, 74, 75, 76, 78, 79, 81, 82, 83, 84, 86, 87

Offset

1,2

Links

G. C. Greubel, 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

From Chai Wah Wu, May 30 2016: (Start)

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

G.f.: x*(x^6 + x^5 + 2*x^4 + x^3 + x^2 + x + 1)/(x^7 - x^6 - x + 1). (End)

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

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-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) = (3*sqrt(2)-1)*Pi/16 + log(2)/4 + sqrt(2)*log(3-2*sqrt(2))/16. - Amiram Eldar, Dec 28 2021

Maple

A047519:=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(A047519(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016

Mathematica

LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {1, 2, 3, 4, 6, 7, 9}, 50] (* G. C. Greubel, May 30 2016 *)

Prog

(Magma) [n : n in [0..100] | n mod 8 in [1, 2, 3, 4, 6, 7]]; // Wesley Ivan Hurt, Jun 16 2016

Crossrefs

Cf. A047422, A047504.

Sequence in context: A285974 A227194 A039054 * A070118 A070124 A059097

Adjacent sequences: A047516 A047517 A047518 * A047520 A047521 A047522

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved