A131028 Periodic sequence (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, 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, 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, 1, 4, 7, 7, 4, 1

Offset: 1

Author

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

Keywords

• nonn
• easy

Comments

Fourth column of triangular array T defined in A131022.

Continued fractions of (131 + sqrt(18530))/37 = 7.2195930... - R. J. Mathar, Mar 08 2012

Links

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

Crossrefs

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

Programs

Magma

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

Mathematica

PadRight[{},120,{7,4,1,1,4,7}] (* Harvey P. Dale, Jul 15 2013 *)

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)), ","))}

Formula

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

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

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

a(n) = 4+2*sqrt(3)*cos(Pi/6*(2*n-1)). - Werner Schulte, Jul 21 2017