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

0,2

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.

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A348013 A105033 A092486 * A119263 A028412 A156699

Adjacent sequences: A159963 A159964 A159965 * A159967 A159968 A159969

Keyword

easy,nonn,less,base

Author

Philippe Deléham, Apr 28 2009

Status

approved