A011765 Period 4: repeat [0, 0, 0, 1].

0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Arises in connection with leap years, years of U.S. Presidential elections, Olympic Games, etc.

Note that leap years define a sequence with period length 400, unlike A121262 which has period length 4. - R. J. Mathar, Dec 19 2008

Links

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

Crossrefs

A121262 is another version.

Programs

Magma

&cat [[0, 0, 0, 1]^^30]; // Wesley Ivan Hurt, Jul 10 2016

Maple

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

Mathematica

PadRight[{}, 120, {0,0,0,1}] (* or *) LinearRecurrence[{0,0,0,1}, {0,0,0,1}, 120] (* Harvey P. Dale, Aug 20 2012 *)

PARI

a(n)=n%4==0 \\ Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: x^4/(1-x^4). - Mohammad K. Azarian, Dec 23 2008

a(n) = (1+(-1)^n)*(1+i^n)/4 with i=sqrt(-1). - Bruno Berselli, Mar 14 2011

a(n) = 1/4 - sin(Pi*(n-1)/2)/2 + (-1)^n/4. - R. J. Mathar, Oct 08 2011

The characteristic function of numbers that are multiples of 4. For the general case: the characteristic function of numbers that are multiples of m is a(n) = floor(n/m) - floor((n-1)/m), m,n > 0. - Boris Putievskiy, May 08 2013

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