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 A265667 Permutation of nonnegative integers: a(n) = n + floor(n/3)*(-1)^(n mod 3). 11
 0, 1, 2, 4, 3, 6, 8, 5, 10, 12, 7, 14, 16, 9, 18, 20, 11, 22, 24, 13, 26, 28, 15, 30, 32, 17, 34, 36, 19, 38, 40, 21, 42, 44, 23, 46, 48, 25, 50, 52, 27, 54, 56, 29, 58, 60, 31, 62, 64, 33, 66, 68, 35, 70, 72, 37, 74, 76, 39, 78, 80, 41, 82, 84, 43, 86, 88, 45 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The inverse permutation is given by P(n) = A006368(n-1) + 1, for n >= 1, and P(0) = 0. - Wolfdieter Lang, Sep 21 2021 This permutation is given by A006369(n-1) + 1, with A006369(-1) = -1. Observed by Kevin Ryde. - Wolfdieter Lang, Sep 22 2021 LINKS Bruno Berselli, Table of n, a(n) for n = 0..1000 Peter Lynch and Michael Mackey, Parity and Partition of the Rational Numbers, arXiv:2205.00565 [math.NT], 2022. See set F p. 4. Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1). FORMULA G.f.: x*(1 + 2*x + 4*x^2 + x^3 + 2*x^4) / ((1 - x)^2*(1 + x + x^2)^2). a(n) = 2*a(n-3) - a(n-6). a(3*k)   = 4*k; a(3*k+1) = 2*k+1, hence a(3*k+1) = a(3*k)/2 + 1; a(3*k+2) = 4*k+2, hence a(3*k+2) = 2*a(3*k+1) = a(3*k) + 2. Sum_{i=0..n} a(i) = A008738(A032793(n+1)). EXAMPLE ------------------------------------------------------------------------- 0, 1, 2, 3,  4, 5, 6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, ... +  +  +  +   +  +  +   +   +   +   +   +   +   +   +   +   +   +   + 0, 0, 0, 1, -1, 1, 2, -2,  2,  3, -3,  3,  4, -4,  4,  5, -5,  5,  6, ... ------------------------------------------------------------------------- 0, 1, 2, 4,  3, 6, 8,  5, 10, 12,  7, 14, 16,  9, 18, 20, 11, 22, 24, ... ------------------------------------------------------------------------- MATHEMATICA Table[n + Floor[n/3] (-1)^Mod[n, 3], {n, 0, 70}] PROG (Sage) [n+floor(n/3)*(-1)^mod(n, 3) for n in (0..70)] (MAGMA) [n+Floor(n/3)*(-1)^(n mod 3): n in [0..70]]; CROSSREFS Cf. A001477, A006368, A006369. Cf. A064455: n+floor(n/2)*(-1)^(n mod 2). Cf. A265888: n+floor(n/4)*(-1)^(n mod 4). Cf. A265734: n+floor(n/5)*(-1)^(n mod 5). Sequence in context: A272904 A233342 A120233 * A338743 A280866 A280864 Adjacent sequences:  A265664 A265665 A265666 * A265668 A265669 A265670 KEYWORD nonn,easy AUTHOR Bruno Berselli, Dec 12 2015 - based on an idea by Paul Curtz. STATUS approved

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Last modified June 29 09:21 EDT 2022. Contains 354910 sequences. (Running on oeis4.)