A047443 Numbers that are congruent to {3, 5, 6} mod 8.

3, 5, 6, 11, 13, 14, 19, 21, 22, 27, 29, 30, 35, 37, 38, 43, 45, 46, 51, 53, 54, 59, 61, 62, 67, 69, 70, 75, 77, 78, 83, 85, 86, 91, 93, 94, 99, 101, 102, 107, 109, 110, 115, 117, 118, 123, 125, 126, 131, 133, 134, 139, 141, 142, 147, 149, 150, 155, 157, 158

Offset

1,1

Comments

Also, numbers n such that Fibonacci(n) = 2 (mod 3), where Fibonacci = A000045. - M. F. Hasler, Sep 29 2012

Links

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

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Formula

G.f.: x*(1+x)*(2*x^2-x+3)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Dec 07 2011

From Wesley Ivan Hurt, Jun 13 2016: (Start)

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.

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

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

Maple

A047443:=n->2*(12*n-3-6*cos(2*n*Pi/3)+sqrt(3)*sin(2*Pi*n/3))/9: seq(A047443(n), n=1..100); # Wesley Ivan Hurt, Jun 13 2016

Mathematica

Select[Range[150], MemberQ[{3, 5, 6}, Mod[#, 8]]&] (* Harvey P. Dale, Oct 04 2011 *)
LinearRecurrence[{1, 0, 1, -1}, {3, 5, 6, 11}, 100] (* Vincenzo Librandi, Jun 14 2016 *)

Prog

(PARI) is_A047443(n)=bittest(104, n%8) \\ with 104=2^3+2^5+2^6. - M. F. Hasler, Sep 29 2012
(PARI) A047443(n)={n=divrem(n, 3); n[1]*8+[-2, 3, 5][n[2]+1]} \\ M. F. Hasler, Sep 29 2012
(Magma) [n : n in [0..150] | n mod 8 in [3, 5, 6]]; // Wesley Ivan Hurt, Jun 13 2016

Crossrefs

Cf. A000045.

Sequence in context: A080759 A145714 A326310 * A173593 A268495 A127577

Adjacent sequences: A047440 A047441 A047442 * A047444 A047445 A047446

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved