A279318 Permutation of the nonnegative integers [6k+3, 6k+2, 6k+1, 6k, 6k+5, 6k+4].

3, 2, 1, 0, 5, 4, 9, 8, 7, 6, 11, 10, 15, 14, 13, 12, 17, 16, 21, 20, 19, 18, 23, 22, 27, 26, 25, 24, 29, 28, 33, 32, 31, 30, 35, 34, 39, 38, 37, 36, 41, 40, 45, 44, 43, 42, 47, 46, 51, 50, 49, 48, 53, 52, 57, 56, 55, 54, 59, 58, 63, 62, 61, 60, 65, 64, 69

Offset

0,1

Links

Table of n, a(n) for n=0..66.

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

Index entries for sequences that are permutations of the natural numbers.

Formula

a(n) = 1 + abs(n - 2 - 6*round((2n - 3)/6)) for n > 3.

G.f.: (3-x-x^2-x^3+5*x^4-x^5+2*x^6)/(1-x-x^6+x^7). - Robert Israel, Dec 13 2016

Sum_{n>=0, n!=3} (-1)^n/a(n) = log(2) (A002162). - Amiram Eldar, Dec 25 2023

Maple

f:= gfun:-rectoproc({a(n+7)-a(n+6)-a(n+1)+a(n)=0, seq(a(i)=[3, 2, 1, 0, 5, 4, 9][i+1], i=0..6)}, a(n), remember):
map(f, [$0..100]); # Robert Israel, Dec 13 2016

Mathematica

Reverse/@TakeDrop[#, 4]&/@Partition[Range[0, 80], 6]//Flatten (* Requires Mathematica version 10 or later *) (* or *) LinearRecurrence[ {1, 0, 0, 0, 0, 1, -1}, {3, 2, 1, 0, 5, 4, 9}, 80] (* Harvey P. Dale, Dec 16 2017 *)

Prog

(Magma) &cat[[6*k+3, 6*k+2, 6*k+1, 6*k, 6*k+5, 6*k+4] : k in [0..20]];

Crossrefs

Cf. A002162, A263824.

Sequence in context: A128317 A344348 A179753 * A084269 A051427 A194763

Adjacent sequences: A279315 A279316 A279317 * A279319 A279320 A279321

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Dec 09 2016

Status

approved