A159966 Lodumo_4 of A102370 (sloping binary numbers).

0, 3, 2, 1, 4, 7, 6, 5, 8, 11, 10, 9, 12, 15, 14, 13, 16, 19, 18, 17, 20, 23, 22, 21, 24, 27, 26, 25, 28, 31, 30, 29, 32, 35, 34, 33, 36, 39, 38, 37, 40, 43, 42, 41, 44, 47, 46, 45, 48, 51, 50, 49, 52, 55, 54, 53, 56, 59, 58, 57, 60, 63, 62, 61, 64, 67, 66, 65, 68, 71, 70, 69, 72

Offset: 0

Author

Philippe Deléham, Apr 28 2009

Keywords

• easy
• nonn
• less
• base

Comments

A permutation of the nonnegative integers.

A092486 preceded by a zero. - Philippe Deléham, May 05 2009

Fixed points are the even numbers. - Wesley Ivan Hurt, Oct 16 2015

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• OEIS wiki, Lodumo transform.
• Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).
• Index entries for sequences that are permutations of the natural numbers.

Crossrefs

Cf. A002162, A005843, A102370, A132429, A158459, A166549.

Programs

Magma

[n-(1-(-1)^n)*(-1)^((2*n+1-(-1)^n) div 4) : n in [0..100]]; // Wesley Ivan Hurt, Oct 16 2015

Maple

A159966:=n->n-(1-(-1)^n)*(-1)^((2*n+1-(-1)^n)/4): seq(A159966(n), n=0..100); # Wesley Ivan Hurt, Oct 16 2015

Mathematica

Table[n - (1 - (-1)^n) (-1)^((2 n + 1 - (-1)^n)/4), {n, 0, 40}] (* or *) CoefficientList[Series[(3 x - 4 x^2 + 3 x^3)/((x - 1)^2 (1 + x^2)), {x, 0, 100}], x] (* Wesley Ivan Hurt, Oct 16 2015 *)
LinearRecurrence[{2,-2,2,-1},{0,3,2,1},80] (* Harvey P. Dale, Jul 02 2022 *)

PARI

concat(0, Vec((3*x-4*x^2+3*x^3)/((x-1)^2*(1+x^2)) + O(x^100))) \\ Altug Alkan, Oct 17 2015

Formula

a(n) = lod_4 (A102370(n)).

From Wesley Ivan Hurt, Oct 16 2015: (Start)

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

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

a(n) = n-(1-(-1)^n)*(-1)^((2*n+1-(-1)^n)/4).

a(2n) = A005843(n); a(2n+1) = A166549(n).

a(n+1) - a(n) = A132429(n)*(-1)^n. (End)

Sum_{n>=1} (-1)^(n+1)/a(n) = log(2) (A002162). - Amiram Eldar, Nov 28 2023