A131800 Period 4: repeat [1, 2, 5, 6].

1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6, 1, 2, 5, 6

Offset: 0

Author

Salvatore Gambino (salvatore.gambino(AT)fastwebnet.it), Oct 04 2007

Keywords

• nonn
• easy

Comments

Decimal expansion of 1256/9999. - Klaus Brockhaus, May 20 2010

Links

• Salvatore Gambino, Terne pitagoriche primitive (in Italian).
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,1).

Crossrefs

Cf. A000111, A178131 (decimal expansion of (11+3*sqrt(21))/17).

Programs

Magma

&cat [[1, 2, 5, 6]^^30]; // Wesley Ivan Hurt, Jul 10 2016

Maple

seq(op([1, 2, 5, 6]), n=0..50); # Wesley Ivan Hurt, Jul 10 2016

Mathematica

PadRight[{}, 100, {1, 2, 5, 6}] (* Wesley Ivan Hurt, Jul 10 2016 *)

PARI

a(n)=[1,2,5,6][n%4+1] \\ Charles R Greathouse IV, Oct 07 2015

Python

def A131800(n): return (1,2,5,6)[n&3] # Chai Wah Wu, Apr 18 2023

Formula

a(n) = (7 + (-1)^n + 4*(-1)^(2*n + 1 - (-1)^n)/4)/2.

G.f.: (1 + 2*x + 5*x^2 + 6*x^3)/((1-x)*(x+1)*(x^2+1)). - R. J. Mathar, Jan 13 2008

a(n) = A000111(n+2) mod 10.

a(n) = 7/2 - 2*cos(Pi*n/2) - 2*sin(Pi*n/2) - (-1)^n/2. - R. J. Mathar, Oct 08 2011

a(n) = a(n-4) for n>3. - Wesley Ivan Hurt, Jul 10 2016

Extensions

More terms from R. J. Mathar, Jan 13 2008