A065261 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.

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, 15, 8, 16, 33, 17, 9, 18, 37, 19, 10, 20, 41, 21, 11, 22, 45, 23, 12, 24, 49, 25, 13, 26, 53, 27, 14, 28, 57, 29, 15, 30, 61, 31, 16, 32, 65, 33, 17, 34, 69, 35, 18, 36, 73, 37, 19, 38

Offset: 1

Author

Antti Karttunen, Oct 28 2001

Keywords

• nonn

Crossrefs

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

Formula

a(2n+2) = n+1, a(4n+1) = 4n+1, a(4n+3) = n+1. - Ralf Stephan, Jun 10 2005

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]

From Luce ETIENNE, Feb 01 2017 : (Start)

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

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.

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