A245477 Period 6: repeat [1, 1, 1, 1, 1, 2].

1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1

Offset: 0

Author

Hailey R. Olafson, Jul 23 2014

Keywords

• nonn
• easy

Comments

First differences of A047368. The first differences of this sequence are in A131533. - Wesley Ivan Hurt, Jul 24 2014

Binomial Transform of a(n) gives: 1, 2, 4, 8, 16, 33, 70, 149, 312, 638, 1276, 2511, ... - Wesley Ivan Hurt, Aug 13 2014

Links

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

Crossrefs

Cf. A024643, A047368, A097325, A130782, A131534, A172051, A177702, A177704, A177706.

Programs

Magma

[Floor((n+1)*7/6) - Floor((n)*7/6) : n in [0..100]]; // Wesley Ivan Hurt, Aug 06 2014

Maple

A:= n -> piecewise(n mod 6 = 5, 2, 1);
seq(A(n), n=0..100); # Robert Israel, Jul 23 2014

Mathematica

Table[2 - Sign[Mod[n + 1, 6]], {n, 0, 100}] (* Wesley Ivan Hurt, Jul 24 2014 *)
PadRight[{},120,{1,1,1,1,1,2}] (* Harvey P. Dale, Jun 02 2016 *)

PARI

a(n) = 7*(n+1)\6 - 7*n\6; \\ Michel Marcus, Jul 23 2014

Sage

[floor((n+1)*7/6) - floor((n)*7/6) for n in [0..200]]

Formula

a(n) = floor((n+1)*7/6) - floor((n)*7/6).

G.f.: 1/(1-x) + x^5/(1-x^6). - Robert Israel, Jul 23 2014

From Wesley Ivan Hurt, Jul 24 2014, Aug 06-29 2014: (Start)

a(n) = 2 - sign((n+1) mod 6).

a(n) = 3 - 2^sign((n+1) mod 6).

a(n) = A172051(n) + 1.

a(2n) = 1, a(2n+1) = A177702(n).

Sum_{i=0..n-2} a(i) = A047368(n), n>0.

a(n) = 1 + mod(n, 1 + mod(n-1, 3)).

a(n) = 1 + binomial(mod(5n + 10, 6), 5). (End)

From Wesley Ivan Hurt, Jun 23 2016: (Start)

a(n) = a(n-6) for n>5.

a(n) = (7 - cos(n*Pi) + cos(n*Pi/3) - cos(2*n*Pi/3) - sqrt(3)*sin(n*Pi/3) - sqrt(3)*sin(2*n*Pi/3))/6. (End)