A154571 Numbers that are congruent to {0, 3, 4, 5, 7, 8} mod 12.

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

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)

Sum_{n>=2} (-1)^n/a(n) = (15-8*sqrt(3))*Pi/72 + log(2)/4. - Amiram Eldar, Dec 31 2021

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