A131030 Period 6: repeat [16, 7, 7, 16, 25, 25].

16, 7, 7, 16, 25, 25, 16, 7, 7, 16, 25, 25, 16, 7, 7, 16, 25, 25, 16, 7, 7, 16, 25, 25, 16, 7, 7, 16, 25, 25, 16, 7, 7, 16, 25, 25, 16, 7, 7, 16, 25, 25, 16, 7, 7, 16, 25, 25, 16, 7, 7, 16, 25, 25, 16, 7, 7, 16, 25, 25, 16, 7, 7, 16, 25, 25, 16, 7, 7, 16, 25, 25, 16, 7, 7, 16, 25, 25, 16

Offset: 1

Author

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

Keywords

• nonn
• easy

Comments

Sixth 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, A131029.

Programs

Magma

m:=79; [ [16, 7, 7, 16, 25, 25][(n-1) mod 6 + 1]: n in [1..m] ];

Maple

seq(op([16, 7, 7, 16, 25, 25]), n=0..30); # Wesley Ivan Hurt, Oct 02 2018

PARI

{m=79; for(n=1, m, r=(n-1)%6; print1(if(r==0||r==3, 16, if(r==1||r==2, 7, 25)), ","))}

Formula

a(1) = a(4) = 16, a(2) = a(3) = 7, a(5) = a(6) = 25; for n > 6, a(n) = a(n-6).

G.f.: x*(16 - 25*x + 25*x^2)/((1-x)*(1 - x + x^2)).

a(n) = 16 + 9*cos(n*Pi/3) - 3*sqrt(3)*sin(n*Pi/3). - Wesley Ivan Hurt, Sep 26 2018