A215898 a(4n) = 1+4n, a(1+4n) = -2-6n, a(2+4n) = 4+6n, a(3+4n) = -3-4n.

1, -2, 4, -3, 5, -8, 10, -7, 9, -14, 16, -11, 13, -20, 22, -15, 17, -26, 28, -19, 21, -32, 34, -23, 25, -38, 40, -27, 29, -44, 46, -31, 33, -50, 52, -35, 37, -56, 58, -39, 41, -62, 64, -43, 45, -68, 70, -47, 49, -74, 76, -51, 53, -80, 82, -55, 57, -86, 88, -59

Offset

0,2

Comments

A permutation of A047253, numbers that are not divisible by 6.

Links

Bruno Berselli, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = 2*a(n-4) - a(n-8).

a(2*n) + a(1+2*n) = -A109613(n)*(-1)^n.

a(3*n) + a(1+3*n) + a(2+3*n) = 3*a(n).

a(4*n) + a(1+4*n) + a(2+4*n) + a(3+4*n) = 0.

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

From Bruno Berselli, Sep 07 2012: (Start)

G.f.: (1-x+3*x^2+3*x^4-x^5+x^6)/((1-x)*(1+x+x^2+x^3)^2).

a(n) = 1+(5-i^(n*(n+1)))*((2*n+1)*(-1)^n-1)/8, where i=sqrt(-1).

a(2*n) = 1+(5-(-1)^n)*n/2; a(2*n+1) = 1-(5+(-1)^n)*(n+1)/2.

a(n) = a(-n-1) = -a(n-1)-a(n-2)-a(n-3)+a(n-4)+a(n-5)+a(n-6)+a(n-7). (End)

Mathematica

a[n_ /; Mod[n, 4] == 0] := n+1; a[n_ /; Mod[n, 4] == 1] := -(3n+1)/2; a[n_ /; Mod[n, 4] == 2] := (3n+2)/2; a[n_ /; Mod[n, 4] == 3] := -n; Table[a[n], {n, 0, 70}] (* Jean-François Alcover, Sep 03 2012 *)
LinearRecurrence[{-1, -1, -1, 1, 1, 1, 1}, {1, -2, 4, -3, 5, -8, 10}, 60] (* Harvey P. Dale, Mar 24 2023 *)

Prog

(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x+3*x^2+3*x^4-x^5+x^6)/((1-x)*(1+x+x^2+x^3)^2))); // Bruno Berselli, Sep 06 2012
(Maxima) makelist(expand(1+(5-%i^(n*(n+1)))*((2*n+1)*(-1)^n-1)/8), n, 0, 60); /* Bruno Berselli, Sep 07 2012 */

Crossrefs

Cf. A016813, A016933, A016957, A004767.

Sequence in context: A222599 A249683 A360434 * A246162 A243573 A132193

Adjacent sequences: A215895 A215896 A215897 * A215899 A215900 A215901

Keyword

sign,easy

Author

Paul Curtz, Aug 25 2012

Status

approved