A177706 Period 5: repeat [1, 1, 1, 1, 2].

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

Offset: 0

Author

Klaus Brockhaus, May 11 2010

Keywords

• nonn
• cofr
• easy

Comments

Continued fraction expansion of (5+sqrt(65))/8.

Decimal expansion of 3704/33333.

Links

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

Crossrefs

Cf. A130782 (repeat 1, 1, 2, 1, 1), A177707 (decimal expansion of (5+sqrt(65))/8).

Programs

Magma

&cat[ [1, 1, 1, 1, 2]: k in [1..21] ];

Maple

A177706:=n->floor(6*(n+1)/5)-floor(6*n/5): seq(A177706(n), n=0..100); # Wesley Ivan Hurt, Jul 24 2014

Mathematica

Table[Floor[6 (n + 1)/5] - Floor[6 n/5], {n, 0, 100}] (* Wesley Ivan Hurt, Jul 24 2014 *)

Formula

a(n) = a(n-5) for n > 4; a(0) = 1, a(1) = 1, a(2) = 1, a(3) = 1, a(4) = 2.

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

a(n) = A130782(n+3).

a(n+4) = A198517(n+2) + A198517(n+1) + A198517(n). - Bruno Berselli, Nov 02 2011

a(n) = floor((n+1)*6/5) - floor((n)*6/5). - Hailey R. Olafson, Jul 23 2014

a(n) = (2/5)*(3 + cos(4*(n-4)*Pi/5) + cos(2*(n+1)*Pi/5)). - Wesley Ivan Hurt, Oct 05 2018

a(n) = 2 - ((n+1)^4 mod 5). - Aaron J Grech, Aug 30 2024