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A159966 Lodumo_4 of A102370 (sloping binary numbers). 4
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..72.

OEIS wiki, Lodumo transform

Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).

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)

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 *)

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. A005843, A102370, A132429, A158459, A166549.

Sequence in context: A208153 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

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Last modified November 23 20:23 EST 2017. Contains 295141 sequences.