A047549 Numbers that are congruent to {0, 1, 2, 3, 4, 7} mod 8.

0, 1, 2, 3, 4, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 27, 28, 31, 32, 33, 34, 35, 36, 39, 40, 41, 42, 43, 44, 47, 48, 49, 50, 51, 52, 55, 56, 57, 58, 59, 60, 63, 64, 65, 66, 67, 68, 71, 72, 73, 74, 75, 76, 79, 80, 81, 82, 83, 84, 87, 88

Offset

1,3

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 29 2016: (Start)

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

G.f.: x^2*(x^5 + 3*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-33+3*cos(n*Pi)+4*sqrt(3)*cos((1-4*n)*Pi/6)+12*sin((1+

2*n)*Pi/6))/18.

a(6k) = 8k-1, a(6k-1) = 8k-4, 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) = (14-sqrt(2))*log(2)/16 + sqrt(2)*log(sqrt(2)+2)/8 - (2-sqrt(2))*Pi/16. - Amiram Eldar, Dec 26 2021

Maple

A047549:=n->(24*n-33+3*cos(n*Pi)+4*sqrt(3)*cos((1-4*n)*Pi/6)+12*sin((1+
2*n)*Pi/6))/18: seq(A047549(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016

Mathematica

LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 1, 2, 3, 4, 7, 8}, 50] (* G. C. Greubel, May 29 2016 *)

Prog

(Magma) [n : n in [0..100] | n mod 8 in [0..4] cat [7]]; // Wesley Ivan Hurt, May 29 2016

Crossrefs

Cf. A047420, A047602.

Sequence in context: A351173 A039146 A039106 * A039074 A326966 A326784

Adjacent sequences: A047546 A047547 A047548 * A047550 A047551 A047552

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved