A047581 Numbers that are congruent to {0, 1, 2, 5, 6, 7} mod 8.

0, 1, 2, 5, 6, 7, 8, 9, 10, 13, 14, 15, 16, 17, 18, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33, 34, 37, 38, 39, 40, 41, 42, 45, 46, 47, 48, 49, 50, 53, 54, 55, 56, 57, 58, 61, 62, 63, 64, 65, 66, 69, 70, 71, 72, 73, 74, 77, 78, 79, 80, 81, 82, 85, 86, 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 30 2016: (Start)

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

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

a(n) = (8*n + (-1)^n - 2*sqrt(3)*sin(Pi*n/3) - 4*sin(2*Pi*(n+1)/3)/sqrt(3) + 2*cos(Pi*n/3) - 7)/6. - Ilya Gutkovskiy, May 30 2016

a(6k) = 8k-1, a(6k-1) = 8k-2, a(6k-2) = 8k-3, a(6k-3) = 8k-6, a(6k-4) = 8k-7, a(6k-5) = 8k-8. - Wesley Ivan Hurt, Jun 16 2016

Sum_{n>=2} (-1)^n/a(n) = (12-sqrt(2))*log(2)/16 + sqrt(2)*log(sqrt(2)+2)/8 - (sqrt(2)-1)*Pi/16. - Amiram Eldar, Dec 27 2021

Maple

A047581:=n->(8*n+(-1)^n-2*sqrt(3)*sin(Pi*n/3)-4*sin(2*Pi*(n+1)/3)/sqrt(3)
+2*cos(Pi*n/3)-7)/6: seq(A047581(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016

Mathematica

LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 1, 2, 5, 6, 7, 8}, 50] (* G. C. Greubel, May 30 2016 *)

Prog

(Magma) [n : n in [0..100] | n mod 8 in [0, 1, 2, 5, 6, 7]]; // Wesley Ivan Hurt, Jun 16 2016

Crossrefs

Cf. A047498, A047513.

Sequence in context: A073416 A138100 A039097 * A039067 A202114 A228090

Adjacent sequences: A047578 A047579 A047580 * A047582 A047583 A047584

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved