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A065173
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Site swap sequence that rises infinitely after t=0. The associated delta sequence p(t)-t for the permutation of Z: A065171.
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3
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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
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OFFSET
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1,3
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COMMENTS
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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.
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LINKS
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FORMULA
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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) = (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
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EXAMPLE
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G.f. = x^2 + 2*x^3 + 2*x^4 + x^5 + 3*x^6 + 6*x^7 + 4*x^8 + 2*x^9 + ...
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MAPLE
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[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);
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PROG
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(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 */
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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