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A265667 Permutation of nonnegative integers: a(n) = n + floor(n/3)*(-1)^(n mod 3). 6
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

LINKS

Bruno Berselli, Table of n, a(n) for n = 0..1000

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.

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 * A280866 A280864 A266411

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 November 13 12:45 EST 2019. Contains 329094 sequences. (Running on oeis4.)