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

Author

Wesley Ivan Hurt, Dec 09 2016

Keywords

• nonn
• easy

Links

• 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.

Crossrefs

Cf. A002162, A263824.

Programs

Magma

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

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 *)

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