A010885 Period 6: repeat [1, 2, 3, 4, 5, 6].

1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Partial sums are given by A130484(n)+n+1. - Hieronymus Fischer, Jun 08 2007

41152/333333 = 0.123456123456123456... [Eric Desbiaux, Nov 03 2008]

Links

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

Crossrefs

Cf. A010872, A010873, A010874, A010875, A010876, A004526, A002264, A002265, A002266.

Cf. A177158 (decimal expansion of (103+2*sqrt(4171))/162). [From Klaus Brockhaus, May 03 2010]

Programs

Magma

&cat[[1..6]: n in [0..20]]; // Wesley Ivan Hurt, Jun 17 2016

Maple

A010885:=n->(21-3*cos(n*Pi)-4*sqrt(3)*cos((1-4*n)*Pi/6)-12*sin((1+2*n)*Pi/6))/6: seq(A010885(n), n=0..100); # Wesley Ivan Hurt, Jun 17 2016

Mathematica

Flatten[Table[Range[6],{n,15}]] (* Harvey P. Dale, Aug 01 2011 *)
PadRight[{},90,Range[6]] (* Harvey P. Dale, Sep 23 2019 *)

Formula

a(n) = 1 + (n mod 6). - Paolo P. Lava, Nov 21 2006

a(n) = A010875(n)+1. G.f.: g(x)=(Sum_{0<=k<6} (k+1)*x^k)/(1-x^6). Also g(x)=(6*x^7-7*x^6+1)/((1-x^6)*(1-x)^2). - Hieronymus Fischer, Jun 08 2007

From Wesley Ivan Hurt, Jun 17 2016: (Start)

G.f.: (1+2*x+3*x^2+4*x^3+5*x^4+6*x^5)/(1-x^6).

a(n) = (21-3*cos(n*Pi)-4*sqrt(3)*cos((1-4*n)*Pi/6)-12*sin((1+2*n)*Pi/6))/6.

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