login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A065173
Site swap sequence that rises infinitely after t=0. The associated delta sequence p(t)-t for the permutation of Z: A065171.
3
0, 1, 2, 2, 1, 3, 6, 4, 2, 5, 10, 6, 3, 7, 14, 8, 4, 9, 18, 10, 5, 11, 22, 12, 6, 13, 26, 14, 7, 15, 30, 16, 8, 17, 34, 18, 9, 19, 38, 20, 10, 21, 42, 22, 11, 23, 46, 24, 12, 25, 50, 26, 13, 27, 54, 28, 14, 29, 58, 30, 15, 31, 62, 32, 16, 33, 66, 34, 17, 35, 70, 36, 18, 37, 74, 38
OFFSET
1,3
COMMENTS
Here the site swap pattern ..., 5, 18, 4, 14, 3, 10, 2, 6, 1, 2, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ... that spans over the Z (zero throw is at t=0) has been folded to N by picking values at t=0, t=1, t=-1, t=2, t=-2, t=3, t=-3, etc. successively.
LINKS
Joe Buhler and R. L. Graham, Juggling Drops and Descents, Amer. Math. Monthly, 101, (no. 6) 1994, 507 - 519.
FORMULA
a(2*k+2) = k+1, a(4*k+1) = k, a(4*k+3) = 4*k+2. - Ralf Stephan, Jun 10 2005
G.f.: x^2*(2*x^5+x^4+x^3+2*x^2+2*x+1) / ((x-1)^2*(x+1)^2*(x^2+1)^2). - Colin Barker, Feb 18 2013
a(n) = 2*a(n-4)-a(n-8) for n>8. - Colin Barker, Oct 29 2016
a(n) = (9*n-5-(n-5)*(-1)^n-3*(n-1)*(1-(-1)^n)*(-1)^((2*n-1+(-1)^n)/4))/16. - Luce ETIENNE, Oct 29 2016
EXAMPLE
G.f. = x^2 + 2*x^3 + 2*x^4 + x^5 + 3*x^6 + 6*x^7 + 4*x^8 + 2*x^9 + ...
MAPLE
[seq((InfRisingSS(N2Z(n))-N2Z(n)), n=1..120)]; N2Z := n -> ((-1)^n)*floor(n/2); Z2N := z -> 2*abs(z)+`if`((z < 1), 1, 0);
PROG
(PARI) concat(0, Vec(x^2*(2*x^5+x^4+x^3+2*x^2+2*x+1)/((x-1)^2*(x+1)^2*(x^2+1)^2) + O(x^100))) \\ Colin Barker, Oct 29 2016
(PARI) {a(n) = if( n%2==0, n/2, n%4==1, n\4, n-1)}; /* Michael Somos, Nov 06 2016 */
CROSSREFS
The other bisection gives A000027.
Sequence in context: A318607 A340106 A259824 * A330965 A098474 A153199
KEYWORD
nonn,easy
AUTHOR
Antti Karttunen, Oct 19 2001
STATUS
approved