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A265734
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Permutation of nonnegative integers: a(n) = n + floor(n/5)*(-1)^(n mod 5).
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6
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0, 1, 2, 3, 4, 6, 5, 8, 7, 10, 12, 9, 14, 11, 16, 18, 13, 20, 15, 22, 24, 17, 26, 19, 28, 30, 21, 32, 23, 34, 36, 25, 38, 27, 40, 42, 29, 44, 31, 46, 48, 33, 50, 35, 52, 54, 37, 56, 39, 58, 60, 41, 62, 43, 64, 66, 45, 68, 47, 70, 72, 49, 74, 51, 76, 78, 53, 80
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OFFSET
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0,3
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,2,0,0,0,0,-1).
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FORMULA
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G.f.: x*(1 + 2*x + 3*x^2 + 4*x^3 + 6*x^4 + 3*x^5 + 4*x^6 + x^7 + 2*x^8) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)^2).
a(n) = 2*a(n-5) - a(n-10).
a(5*k+r) = (5+(-1)^r)*k + r, where r=0..4.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi*(1/(2*sqrt(2))-1/(3*sqrt(3))) + log(2)/6. - 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, 0, 0, 1, -1, 1, -1, 1, 2, -2, 2, -2, 2, 3, -3, 3, -3, ...
------------------------------------------------------------------------
0, 1, 2, 3, 4, 6, 5, 8, 7, 10, 12, 9, 14, 11, 16, 18, 13, 20, 15, ...
------------------------------------------------------------------------
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MATHEMATICA
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Table[n + Floor[n/5] (-1)^Mod[n, 5], {n, 0, 80}]
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PROG
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(Sage) [n+floor(n/5)*(-1)^mod(n, 5) for n in (0..80)]
(Magma) [n+Floor(n/5)*(-1)^(n mod 5): n in [0..80]];
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CROSSREFS
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Cf. A064455: n+floor(n/2)*(-1)^(n mod 2).
Cf. A265667: n+floor(n/3)*(-1)^(n mod 3).
Cf. A265888: n+floor(n/4)*(-1)^(n mod 4)
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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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