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%I #21 Apr 08 2024 17:46:24
%S 0,1,0,1,1,1,2,1,3,2,4,4,6,7,10,11,17,17,28,27,45,44,72,72,116,117,
%T 188,189,305,305,494,493,799,798,1292,1292,2090,2091,3382,3383,5473,
%U 5473,8856,8855,14329,14328,23184,23184,37512,37513,60696
%N For n odd a(n) = a(n-2) + a(n-3), for n even a(n) = a(n-2) + a(n-5); with a(1) = 0, a(2) = 1.
%C Combination a(2n)=A005252(n-1) and a(2n+1)=A024490(n). Consecutive pairs add up to A000045 and subtract to A010892. If a(1)= 1 formula gives: A103609.
%H Harvey P. Dale, <a href="/A174618/b174618.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1,0,0,0,1).
%F G.f.: -x^2*(1-x^2+x^3) / ( (x^4-x^2+1)*(x^4+x^2-1) ). - _R. J. Mathar_, Jan 27 2011
%e As consecutive pairs: (0,1),(0,1),(1,1),(2,1),(3,2),(4,4),...
%t nxt[{n_,a_,b_,c_,d_,e_}]:={n+1,b,c,d,e,If[EvenQ[n],d+c,d+a]}; NestList[nxt,{5,0,1,0,1,1},50][[All,2]] (* or *) LinearRecurrence[ {0,2,0,-1,0,0,0,1},{0,1,0,1,1,1,2,1},60] (* _Harvey P. Dale_, Nov 15 2019 *)
%Y Cf. A005252, A024490, A000045, A010892.
%K nonn,easy,changed
%O 1,7
%A _Mark Dols_, Mar 23 2010
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