A263824 Permutation of the nonnegative integers: [6k+3, 6k+4, 6k+5, 6k, 6k+1, 6k+2, ...].

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

Offset: 0

Author

Wesley Ivan Hurt, Oct 27 2015

Keywords

• nonn
• easy
• changed

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-1,-1,2,-1).
• Index entries for sequences that are permutations of the natural numbers.

Crossrefs

Cf. A002162, A004442, A130151, A279318.

Programs

Magma

[n+3*(-1)^Floor(n/3) : n in [0..100]];

Magma

I:=[3,4,5,0,1]; [n le 5 select I[n] else 2*Self(n-1)- Self(n-2)-Self(n-3)+2*Self(n-4)-Self(n-5): n in [1..70]]; // Vincenzo Librandi, Nov 22 2015

Maple

A263824:=n->n+3*(-1)^floor(n/3): seq(A263824(n), n=0..100);

Mathematica

Table[n + 3 (-1)^Floor[n/3], {n, 0, 100}]
CoefficientList[Series[(3 - 2 x - 3 x^3 + 4 x^4)/((x - 1)^2 (1 + x^3)), {x, 0, 70}], x] (* Vincenzo Librandi, Nov 22 2015 *)
LinearRecurrence[{2,-1,-1,2,-1},{3,4,5,0,1},70] (* Harvey P. Dale, Jun 23 2017 *)

PARI

Vec((3-2*x-3*x^3+4*x^4) / ((x-1)^2*(1+x^3)) + O(x^100)) \\ Altug Alkan, Oct 28 2015

PARI

A263824(n)=n+3*(-1)^(n\3) \\ M. F. Hasler, Nov 25 2015

Formula

G.f.: (3-2*x-3*x^3+4*x^4) / ((x-1)^2*(1+x^3)).

a(n) = 2*a(n-1) - a(n-2) - a(n-3) + 2*a(n-4) - a(n-5), n>4.

a(n) = n + 3*(-1)^floor(n/3).

a(n) = a(n-6) + 6 for n>5. - Tom Edgar, Oct 28 2015

From Wesley Ivan Hurt, Nov 22 2015: (Start)

a(n) = n + 3*A130151(n).

a(3n) = 3*A004442(n). (End)

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

E.g.f.: exp(-x) + x*exp(x) + 2*exp(x/2)*(cos(sqrt(3)*x/2) + sqrt(3)*sin(sqrt(3)*x/2)). - Stefano Spezia, Aug 25 2025