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A011765 Period 4: repeat [0, 0, 0, 1]. 10
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

Table of n, a(n) for n=1..96.

Index entries for characteristic functions

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

FORMULA

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

a(n) = (1/24)*{7*(n mod 4)-5*[(n+1) mod 4]+[(n+2) mod 4]+[(n+3) mod 4]}, with n>=0. - Paolo P. Lava, Feb 06 2009

a(n) = (1/4)*(1-(-1)^n+I^(1+n)-I^(1-n)), with n>=0 and I=sqrt(-1). - Paolo P. Lava, May 04 2010

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

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 *)

PROG

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

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

CROSSREFS

A121262 is another version.

Sequence in context: A188291 A287372 A188221 * A285464 A144602 A275855

Adjacent sequences:  A011762 A011763 A011764 * A011766 A011767 A011768

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified April 20 22:22 EDT 2019. Contains 322310 sequences. (Running on oeis4.)