0,1

This sequence can be used to produce a periodic sequence of 4 numbers b,c,d,e: a(n)=b*(1/4)* [2*cos(n*Pi/2)+ 1+(-1)^n]+ c*(1/4)* [2*cos((n+3)*Pi/2)+ 1+(-1)^(n+3)] + d*(1/4)* [2*cos((n+2)*Pi/2)+ 1+(-1)^(n+2)] + e*(1/4)* [2*cos((n+1)*Pi/2)+ 1+(-1)^(n+1)]

a(n) = (1/4)* [2*cos(n*Pi/2)+ 1+(-1)^n]

Additive with a(p^e) = 1 if p = 2 and e > 1, 0 otherwise.

Sequence shifted right by 2 is additive with a(p^e) = 1 if p = 2 and e = 1, 0 otherwise.

a(n)=1-[C(n+1,n+(-1)^(n+1)) mod 2]

a(0)=(1/4)*[2*cos(0)+1+1]= (1/4)*[2+2]= 1

a(1)=(1/4)*[2*cos(Pi/2)+1-1]= (1/4)*[0+0]= 0

a(2)=(1/4)*[2*cos(Pi)+1+1]= (1/4)*[ -2+2]= 0

a(3)=(1/4)*[2*cos(3*Pi/2)+1-1]= (1/4)*[0+0] = 0

P:=proc(n)local i, j; for i from 0 by 1 to n do j:=1/4*(2*cos(i*Pi/2)+1+(-1)^i); print(j); od; end: P(100);

with(combstruct):ZL4:=[S, {S=Set(Cycle(Z, card=4))}, unlabeled]:seq(count(ZL4, size=n), n=0..104); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 24 2007

A011765 is another version of the same sequence.

Sequence in context: A015985 A015777 A014017 this_sequence A102243 A104108 A089024

Adjacent sequences: A121259 A121260 A121261 this_sequence A121263 A121264 A121265

nonn

Paolo P. Lava and Giorgio Balzarotti (ppl(AT)spl.at), Aug 23 2006, Aug 30 2007