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A065171 Permutation of Z, folded to N, corresponding to the site swap pattern ...26120123456... which ascends infinitely after t=0. 6
1, 4, 2, 8, 3, 12, 6, 16, 5, 20, 10, 24, 7, 28, 14, 32, 9, 36, 18, 40, 11, 44, 22, 48, 13, 52, 26, 56, 15, 60, 30, 64, 17, 68, 34, 72, 19, 76, 38, 80, 21, 84, 42, 88, 23, 92, 46, 96, 25, 100, 50, 104, 27, 108, 54, 112, 29, 116, 58, 120, 31, 124, 62, 128, 33, 132, 66, 136, 35 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
This permutation consists of one fixed point (at 0, mapped here to 1) and an infinite number of infinite cycles.
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) = 4*k+4, a(4*k+1) = 2*k+1, a(4*k+3) = 4*k+2. - Ralf Stephan, Jun 10 2005
G.f.: x*(2*x^6+4*x^5+x^4+8*x^3+2*x^2+4*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) = (11*n-1+(5*n+1)*(-1)^n+(n-3)*(1-(-1)^n)*(-1)^((2*n+3+(-1)^n)/4))/8. - Luce ETIENNE, Oct 20 2016
EXAMPLE
G.f. = x + 4*x^2 + 2*x^3 + 8*x^4 + 3*x^5 + 12*x^6 + 6*x^7 + 16*x^8 + ...
MAPLE
[seq(Z2N(InfRisingSS(N2Z(n))), n=1..120)]; InfRisingSS := z -> `if`((z < 0), `if`((0 = (z mod 2)), z/2, -z), 2*z);
N2Z := n -> ((-1)^n)*floor(n/2); Z2N := z -> 2*abs(z)+`if`((z < 1), 1, 0);
PROG
(PARI) Vec(x*(2*x^6+4*x^5+x^4+8*x^3+2*x^2+4*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, n\2+1, n*2)}; /* Michael Somos, Nov 06 2016 */
CROSSREFS
Inverse permutation: A065172. A065173 gives the deltas p(t)-t, i.e., the associated site swap sequence. Cf. also A065167, A065174, A065260.
Sequence in context: A026209 A198473 A133640 * A026192 A026142 A095399
KEYWORD
nonn,easy
AUTHOR
Antti Karttunen, Oct 19 2001
STATUS
approved

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Last modified July 19 04:51 EDT 2024. Contains 374388 sequences. (Running on oeis4.)