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

1,4

Links

Table of n, a(n) for n=1..76.

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)

Crossrefs

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

Sequence in context: A188923 A078375 A362090 * A130848 A222760 A302130

Adjacent sequences: A065258 A065259 A065260 * A065262 A065263 A065264

Keyword

nonn

Author

Antti Karttunen, Oct 28 2001

Status

approved