A096406 - OEIS

A096406

a(1) = 4; then alternately add -4 and multiply by -2.

4, 0, 0, -4, 8, 4, -8, -12, 24, 20, -40, -44, 88, 84, -168, -172, 344, 340, -680, -684, 1368, 1364, -2728, -2732, 5464, 5460, -10920, -10924, 21848, 21844, -43688, -43692, 87384, 87380, -174760, -174764, 349528, 349524, -699048, -699052, 1398104, 1398100, -2796200, -2796204, 5592408, 5592404

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OFFSET

1,1

COMMENTS

Applet randomly selects from among nine algorithms and each algorithm has its own random parameters. Six terms are presented and you get to guess the next term.

LINKS

Table of n, a(n) for n=1..46.

Alexander Bogomolny's Cut-the-Knot.org, What's Next?

Index entries for linear recurrences with constant coefficients, signature (0,-1,0,2).

FORMULA

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

a(n) = (1/3)*(2 - 6(-1)^n - 2(-2)^ceiling(n/2)). - Ralf Stephan, Dec 04 2004

O.g.f.: 4*x*(-1 - x^2 + x^3)/((-1+x)*(1+x)*(1+2*x^2)). - R. J. Mathar, Dec 05 2007

a(n) = -a(n-2) + 2*a(n-4); a(1)=4, a(2)=0, a(3)=0, a(4)=-4. - Harvey P. Dale, May 01 2016

MATHEMATICA

LinearRecurrence[{0, -1, 0, 2}, {4, 0, 0, -4}, 50] (* Harvey P. Dale, May 01 2016 *)

CROSSREFS