%I #21 Jun 25 2023 03:42:25

%S 2,2,4,6,12,20,40,68,136,232,464,792,1584,2704,5408,9232,18464,31520,

%T 63040,107616,215232,367424,734848,1254464,2508928,4283008,8566016,

%U 14623104,29246208,49926400,99852800,170459392,340918784,581984768,1163969536,1987020288

%N Expansion of g.f. (1 + x - 2*x^2 - x^3)/(1/2 - 2*x^2 + x^4).

%C Also (starting 4,6,...) the number of zig-zag paths from top to bottom of a rectangle of width 7, whose color is that of the top right corner. - _Joseph Myers_, Dec 24 2008

%H Harvey P. Dale, <a href="/A030435/b030435.txt">Table of n, a(n) for n = 0..1000</a>

%H Joseph Myers, <a href="http://www.polyomino.org.uk/publications/2008/bmo1-2009-q1.pdf">BMO 2008--2009 Round 1 Problem 1---Generalisation</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,0,-2).

%F E.g.f.: cosh(r*x) + cosh(s*x) + (r*sinh(r*x) + s*sinh(s*x))/2, where r = sqrt(2 - sqrt(2)) and s = sqrt(2 + sqrt(2)). - _Stefano Spezia_, Jun 14 2023

%t CoefficientList[Series[(1+x-2*x^2-x^3)/(1/2-2*x^2+x^4),{x,0,40}],x] (* _Harvey P. Dale_, Oct 05 2020 *)

%o (PARI) Vec((1+x-2*x^2-x^3)/(1/2-2*x^2+x^4)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 27 2012

%Y Twice A030436.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_