A175833 Periodic sequence: repeat 4,7,11.

4, 7, 11, 4, 7, 11, 4, 7, 11, 4, 7, 11, 4, 7, 11, 4, 7, 11, 4, 7, 11, 4, 7, 11, 4, 7, 11, 4, 7, 11, 4, 7, 11, 4, 7, 11, 4, 7, 11, 4, 7, 11, 4, 7, 11, 4, 7, 11, 4, 7, 11, 4, 7, 11, 4, 7, 11, 4, 7, 11, 4, 7, 11, 4, 7, 11, 4, 7, 11, 4, 7, 11, 4, 7, 11, 4, 7, 11, 4, 7, 11, 4, 7, 11, 4, 7, 11

Offset: 0

Author

Bruno Berselli, Sep 17 2010

Keywords

• nonn
• easy

Comments

Continued fraction expansion of (158+sqrt(27226))/78.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,1).

Crossrefs

Cf. A010882, A011655.

Programs

Magma

&cat[[4,7,11]^^30];

Mathematica

PadRight[{},120,{4,7,11}] (* Harvey P. Dale, Jul 17 2013 *)

Maxima

makelist(concat(4,", ",7,", ",11), n, 0, 28); /* Bruno Berselli, Nov 13 2012 */

Python

[4,7,11]*30 # Bruno Berselli, Dec 02 2016

Formula

G.f.: (4 + 7*x + 11*x^2)/(1 - x^3).

a(n) = a(n-3) for n>2.

a(n) = 4*A010882(n) - A011655(n) = 4*(n + 1 - 3*floor(n/3)) - (1 - (-1)^(n-3*floor((n+1)/3)))/2.