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A265667
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Permutation of nonnegative integers: a(n) = n + floor(n/3)*(-1)^(n mod 3).
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11
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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
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OFFSET
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0,3
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COMMENTS
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The inverse permutation is given by P(n) = A006368(n-1) + 1, for n >= 1, and P(0) = 0. - Wolfdieter Lang, Sep 21 2021
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LINKS
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FORMULA
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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_{n>=1} (-1)^(n+1)/a(n) = Pi/8 + log(2)/4. - Amiram Eldar, Mar 30 2023
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EXAMPLE
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-------------------------------------------------------------------------
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, ...
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0, 1, 2, 4, 3, 6, 8, 5, 10, 12, 7, 14, 16, 9, 18, 20, 11, 22, 24, ...
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MATHEMATICA
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Table[n + Floor[n/3] (-1)^Mod[n, 3], {n, 0, 70}]
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PROG
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(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]];
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CROSSREFS
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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).
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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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