A131028 - OEIS

%I #39 Apr 18 2024 09:28:18

%S 7,4,1,1,4,7,7,4,1,1,4,7,7,4,1,1,4,7,7,4,1,1,4,7,7,4,1,1,4,7,7,4,1,1,

%T 4,7,7,4,1,1,4,7,7,4,1,1,4,7,7,4,1,1,4,7,7,4,1,1,4,7,7,4,1,1,4,7,7,4,

%U 1,1,4,7,7,4,1,1,4,7,7,4,1,1,4,7,7,4,1,1,4,7,7,4,1,1,4,7,7,4,1,1,4,7,7,4,1

%N Periodic sequence (7, 4, 1, 1, 4, 7).

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

%C Continued fractions of (131 + sqrt(18530))/37 = 7.2195930... - _R. J. Mathar_, Mar 08 2012

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

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

%F G.f.: x*(7-10*x+7*x^2)/((1-x)*(1-x+x^2)).

%F a(n) = A084104(n+2).

%F a(n) = 4+2*sqrt(3)*cos(Pi/6*(2*n-1)). - _Werner Schulte_, Jul 21 2017

%t PadRight[{},120,{7,4,1,1,4,7}] (* _Harvey P. Dale_, Jul 15 2013 *)

%o (PARI) {m=105; for(n=1, m, r=(n-1)%6; print1(if(r==0||r==5, 7, if(r==1||r==4, 4, 1)), ","))}

%o (Magma) m:=105; [ [7, 4, 1, 1, 4, 7][(n-1) mod 6 + 1]: n in [1..m] ];

%Y Cf. A131022, A084104. Other columns of T are in A088911, A131026, A131027, A131029, A131030.

%K nonn,easy

%O 1,1

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