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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 Colin Barker, Table of n, a(n) for n = 1..1000 Joe Buhler and R. L. Graham, Juggling Drops and Descents, Amer. Math. Monthly, 101, (no. 6) 1994, 507 - 519. Index entries for sequences that are permutations of the natural numbers Index entries for linear recurrences with constant coefficients, signature (0,0,0,2,0,0,0,-1). 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 Adjacent sequences: A065168 A065169 A065170 * A065172 A065173 A065174 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.)