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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A076840 A188923 A078375 * A130848 A222760 A302130

Adjacent sequences:  A065258 A065259 A065260 * A065262 A065263 A065264

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 28 2001

STATUS

approved

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Last modified February 21 11:25 EST 2019. Contains 320372 sequences. (Running on oeis4.)