A131029 Periodic sequence (11, 5, 2, 5, 11, 14).

11, 5, 2, 5, 11, 14, 11, 5, 2, 5, 11, 14, 11, 5, 2, 5, 11, 14, 11, 5, 2, 5, 11, 14, 11, 5, 2, 5, 11, 14, 11, 5, 2, 5, 11, 14, 11, 5, 2, 5, 11, 14, 11, 5, 2, 5, 11, 14, 11, 5, 2, 5, 11, 14, 11, 5, 2, 5, 11, 14, 11, 5, 2, 5, 11, 14, 11, 5, 2, 5, 11, 14, 11, 5, 2, 5, 11, 14, 11, 5, 2, 5, 11, 14

Offset: 1

Author

Klaus Brockhaus, following a suggestion of Paul Curtz, Jun 10 2007

Keywords

• nonn
• easy

Comments

Fifth column of triangular array T defined in A131022.

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-2,1).

Crossrefs

Cf. A131022. Other columns of T are in A088911, A131026, A131027, A131028, A131030.

Programs

Magma

m:=84; [ [11, 5, 2, 5, 11, 14][(n-1) mod 6 + 1]: n in [1..m] ];

Mathematica

PadRight[{},120,{11,5,2,5,11,14}] (* or *) LinearRecurrence[{2,-2,1},{11,5,2},120] (* Harvey P. Dale, Jun 12 2017 *)

PARI

{m=84; for(n=1, m, r=(n-1)%6; print1(if(r==0||r==4, 11, if(r==2, 2, if(r==5, 14, 5))), ","))}

Python

def a(n): return [11, 5, 2, 5, 11, 14][n%6]
print([a(n) for n in range(84)]) # Michael S. Branicky, Nov 05 2021

Formula

a(1) = a(5) = 11, a(2) = a(4) = 5, a(3) = 2, a(6) = 14; for n > 6, a(n) = a(n-6).

G.f.: (11-17*x+14*x^2)/((1-x)*(1-x+x^2)).

a(n) = 3*cos((n-1)/3*Pi)-3*sqrt(3)*sin((n-1)/3*Pi)+8. - Leonid Bedratyuk, May 13 2012