A065261 - OEIS

%I #17 Feb 01 2017 16:57:57

%S 1,1,1,2,5,3,2,4,9,5,3,6,13,7,4,8,17,9,5,10,21,11,6,12,25,13,7,14,29,

%T 15,8,16,33,17,9,18,37,19,10,20,41,21,11,22,45,23,12,24,49,25,13,26,

%U 53,27,14,28,57,29,15,30,61,31,16,32,65,33,17,34,69,35,18,36,73,37,19,38

%N The siteswap sequence (the deltas p[i]-i, i in ]-inf,+inf[, folded from Z to N, mapping 0->1, 1->2, -1->3, 2->4, -2->5, etc.) for A065260.

%F a(2n+2) = n+1, a(4n+1) = 4n+1, a(4n+3) = n+1. - _Ralf Stephan_, Jun 10 2005

%F Empirical g.f.: x*(x^5+3*x^4+2*x^3+x^2+x+1) / ((x-1)^2*(x+1)^2*(x^2+1)^2). [_Colin Barker_, Feb 18 2013]

%F From _Luce ETIENNE_, Feb 01 2017 : (Start)

%F a(n) = 2*a(n-4)-a(n-8).

%F a(n) = (9*n+1-(n+1)*(-1)^n+(3*n-1)*((-1)^((2*n-1+(-1)^n)/4)-(-1)^((2*n+1-(-1)^n)/4)))/16.

%F a(n) = (9*n+1-(n+1)*cos(n*Pi)+2*(3*n-1)*sin(n*Pi/2))/16. (End)

%Y The bisection giving the positive half of Z is A000027 and the nonpositive half is A065262. Cf. also A065173.

%K nonn

%O 1,4

%A _Antti Karttunen_, Oct 28 2001