A153349 Period 6: repeat [1, 7, 4, 4, 7, 1].

1, 7, 4, 4, 7, 1, 1, 7, 4, 4, 7, 1, 1, 7, 4, 4, 7, 1, 1, 7, 4, 4, 7, 1, 1, 7, 4, 4, 7, 1, 1, 7, 4, 4, 7, 1, 1, 7, 4, 4, 7, 1, 1, 7, 4, 4, 7, 1, 1, 7, 4, 4, 7, 1, 1, 7, 4, 4, 7, 1, 1, 7, 4, 4, 7, 1, 1, 7, 4, 4, 7, 1, 1, 7, 4, 4, 7, 1, 1, 7, 4, 4, 7, 1, 1, 7, 4, 4, 7, 1, 1, 7, 4, 4, 7, 1, 1, 7, 4, 4, 7, 1, 1, 7, 4

Offset: 0

Author

Paul Curtz, Dec 24 2008

Keywords

• nonn
• easy

Comments

Also: the decimal expansion of 5287/30303. [R. J. Mathar, Jan 03 2009]

Links

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

Crossrefs

Cf. A010892, A099837.

Programs

Magma

&cat [[1, 7, 4, 4, 7, 1]^^20]; // Wesley Ivan Hurt, Jun 23 2016

Maple

A153349:=n->[1, 7, 4, 4, 7, 1][(n mod 6)+1]: seq(A153349(n), n=0..100); # Wesley Ivan Hurt, Jun 23 2016

Mathematica

PadRight[{}, 100, {1, 7, 4, 4, 7, 1}] (* Wesley Ivan Hurt, Jun 23 2016 *)

Formula

G.f.: (x^4+6*x^3-2*x^2+6*x+1)/((1-x)*(x^2-x+1)*(1+x+x^2)). a(n) = 4 + 3*A099837(n+2)/2 + 3*A010892(n+4)/2. [R. J. Mathar, Jan 03 2009]

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

a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) for n>4.

a(n) = (8 - 3*cos(n*Pi/3) - 3*cos(2*n*Pi/3) + sqrt(3)*sin(n*Pi/3) + 3*sqrt(3)*sin(2*n*Pi/3))/2. (End)

Extensions

Extended by R. J. Mathar, Jan 03 2009