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A047585 Numbers that are congruent to {0, 1, 3, 5, 6, 7} mod 8. 1
0, 1, 3, 5, 6, 7, 8, 9, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 24, 25, 27, 29, 30, 31, 32, 33, 35, 37, 38, 39, 40, 41, 43, 45, 46, 47, 48, 49, 51, 53, 54, 55, 56, 57, 59, 61, 62, 63, 64, 65, 67, 69, 70, 71, 72, 73, 75, 77, 78, 79, 80, 81, 83, 85, 86, 87, 88 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-2,2,-1).

FORMULA

From Chai Wah Wu, Jun 10 2016: (Start)

a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - a(n-6).

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

a(n) = (12*n - 3*sqrt(3)*sin(Pi*n/3) + sqrt(3)*sin(2*Pi*n/3) - 9)/9. - Ilya Gutkovskiy, Jun 11 2016

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

MAPLE

A047585:=n->(12*n - 3*sqrt(3)*sin(Pi*n/3) + sqrt(3)*sin(2*Pi*n/3) - 9)/9: seq(A047585(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016

MATHEMATICA

Select[Range[0, 100], MemberQ[{0, 1, 3, 5, 6, 7}, Mod[#, 8]]&] (* or *) Complement[Range[0, 100], Flatten[Range[{2, 4}, 100, 8]]] (* Harvey P. Dale, May 01 2012 *)

CoefficientList[Series[x (x^4 + x^2 + x + 1) / ((x - 1)^2 (x^2 - x + 1) (x^2 + x + 1)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 18 2016 *)

PROG

(MAGMA) [n : n in [0..100] | n mod 8 in [0, 1, 3, 5, 6, 7]]; // Wesley Ivan Hurt, Jun 16 2016

CROSSREFS

Sequence in context: A039092 A289178 A212450 * A288224 A039063 A266114

Adjacent sequences:  A047582 A047583 A047584 * A047586 A047587 A047588

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Dec 11 1999

STATUS

approved

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Last modified February 21 03:06 EST 2019. Contains 320364 sequences. (Running on oeis4.)