A131030 - OEIS

%I #33 Apr 18 2024 11:42:14

%S 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,

%T 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,

%U 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

%N Period 6: repeat [16, 7, 7, 16, 25, 25].

%C Sixth column of triangular array T defined in A131022.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,1).

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

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

%F a(n) = 16 + 9*cos(n*Pi/3) - 3*sqrt(3)*sin(n*Pi/3). - _Wesley Ivan Hurt_, Sep 26 2018

%p seq(op([16, 7, 7, 16, 25, 25]), n=0..30); # _Wesley Ivan Hurt_, Oct 02 2018

%o (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)), ","))}

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

%Y Cf. A131022. Other columns of T are in A088911, A131026, A131027, A131028, A131029.

%K nonn,easy

%O 1,1

%A _Klaus Brockhaus_, following a suggestion of _Paul Curtz_, Jun 10 2007