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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 permutations of the positive (or nonnegative) integers.

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.)