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A154571 Numbers that are congruent to {0, 3, 4, 5, 7, 8} mod 12. 1
0, 3, 4, 5, 7, 8, 12, 15, 16, 17, 19, 20, 24, 27, 28, 29, 31, 32, 36, 39, 40, 41, 43, 44, 48, 51, 52, 53, 55, 56, 60, 63, 64, 65, 67, 68, 72, 75, 76, 77, 79, 80, 84, 87, 88, 89, 91, 92, 96, 99, 100, 101, 103, 104, 108, 111, 112, 113, 115, 116, 120, 123, 124 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

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

a(n) = (12*n-15-cos(n*Pi)-5*cos(n*Pi/3)-sqrt(3)*(2*cos((1-4*n)*Pi/6)-3*sin(n*Pi/3)))/6.

a(6k) = 12k-4, a(6k-1) = 12k-5, a(6k-2) = 12k-7, a(6k-3) = 12k-8, a(6k-4) = 12k-9, a(6k-5) = 12k-12. (End)

MAPLE

A154571:=n->(12*n-15-cos(n*Pi)-5*cos(n*Pi/3)-sqrt(3)*(2*cos((1-4*n)*Pi/6)-3*sin(n*Pi/3)))/6: seq(A154571(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016

MATHEMATICA

LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 3, 4, 5, 7, 8, 12}, 50] (* G. C. Greubel, May 29 2016 *)

PROG

(MAGMA) [n : n in [0..150] | n mod 12 in [0, 3, 4, 5, 7, 8]]; // Wesley Ivan Hurt, May 29 2016

CROSSREFS

Cf. A113829.

Sequence in context: A242965 A266796 A318603 * A174269 A112882 A180152

Adjacent sequences:  A154568 A154569 A154570 * A154572 A154573 A154574

KEYWORD

easy,nonn

AUTHOR

Omar E. Pol, Jan 12 2009

STATUS

approved

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Last modified September 19 17:19 EDT 2021. Contains 347564 sequences. (Running on oeis4.)