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

1,1

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

Table of n, a(n) for n=1..105.

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

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

a(n) = 2*a(n-1) - 2*a(n-2) + a(n-3). - Wesley Ivan Hurt, Jun 12 2026

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A082665 A011101 A021935 * A225463 A381685 A010138

Adjacent sequences: A131025 A131026 A131027 * A131029 A131030 A131031

Keyword

nonn,easy,changed

Author

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

Status

approved