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 A011765 Period 4: repeat [0, 0, 0, 1]. 11
 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 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 * A342023 A342024 A285464 Adjacent sequences:  A011762 A011763 A011764 * A011766 A011767 A011768 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified May 16 21:28 EDT 2021. Contains 343951 sequences. (Running on oeis4.)