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A047564 Numbers that are congruent to {1, 3, 4, 5, 6, 7} mod 8. 3
1, 3, 4, 5, 6, 7, 9, 11, 12, 13, 14, 15, 17, 19, 20, 21, 22, 23, 25, 27, 28, 29, 30, 31, 33, 35, 36, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 51, 52, 53, 54, 55, 57, 59, 60, 61, 62, 63, 65, 67, 68, 69, 70, 71, 73, 75, 76, 77, 78, 79, 81, 83, 84, 85, 86, 87 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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, May 30 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) for n>6.

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

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

a(n) = (12*n-3-sqrt(3)*(cos((1-4*n)*Pi/6)+3*cos((1+2*n)*Pi/6)))/9.

a(6k) = 8k-1, a(6k-1) = 8k-2, a(6k-2) = 8k-3, a(6k-3) = 8k-4, a(6k-4) = 8k-5, a(6k-5) = 8k-7. (End)

MAPLE

A047564:=n->(12*n-3-sqrt(3)*(cos((1-4*n)*Pi/6)+3*cos((1+2*n)*Pi/6)))/9: seq(A047564(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016

MATHEMATICA

Select[Range[0, 100], MemberQ[{1, 3, 4, 5, 6, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 16 2016 *)

CoefficientList[Series[(x^5 + x^3 + 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 [1, 3, 4, 5, 6, 7]]; // Wesley Ivan Hurt, Jun 16 2016

CROSSREFS

Sequence in context: A307712 A048869 A039051 * A154536 A298110 A091815

Adjacent sequences:  A047561 A047562 A047563 * A047565 A047566 A047567

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified July 25 13:05 EDT 2021. Contains 346290 sequences. (Running on oeis4.)