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A047581 Numbers that are congruent to {0, 1, 2, 5, 6, 7} mod 8. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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

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

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Last modified August 18 20:02 EDT 2019. Contains 326109 sequences. (Running on oeis4.)