A265734 Permutation of nonnegative integers: a(n) = n + floor(n/5)*(-1)^(n mod 5).

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

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,2,0,0,0,0,-1).

Index entries for permutations of the positive (or nonnegative) integers.

Formula

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

Example

------------------------------------------------------------------------
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, ...
------------------------------------------------------------------------

Mathematica

Table[n + Floor[n/5] (-1)^Mod[n, 5], {n, 0, 80}]

Prog

(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]];

Crossrefs

Cf. A001477.

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)

Sequence in context: A285039 A260307 A285041 * A299759 A372030 A232560

Adjacent sequences: A265731 A265732 A265733 * A265735 A265736 A265737

Keyword

nonn,easy

Author

_Bruno Berselli_, Dec 15 2015 - based on an idea by _Paul Curtz_.

Status

approved