%I #12 Dec 21 2023 20:57:38

%S 0,0,1,1,2,3,6,11,20,37,69,126,232,426,784,1442,2652,4878,8973,16503,

%T 30354,55829,102686,188869,347384,638939,1175193,2161516,3975648,

%U 7312356,13449520,24737524,45499400,83686444,153923369,283109213,520719026,957751607

%N A dihedial D1 elliptical transform on A000073.

%C D1 elliptical invariant transform leaves the ratio unchanged.

%F a(n) = -floor(g(A000073(n))) with g(k) = (k-1)^2/(-4*k).

%F Conjectures from _Chai Wah Wu_, Dec 21 2023: (Start)

%F a(n) = a(n-2) + 2*a(n-3) + 2*a(n-4) + 2*a(n-5) + 2*a(n-6) + 2*a(n-7) + 3*a(n-8) + 2*a(n-9) + a(n-10) for n > 11.

%F G.f.: x^4*(-x^2 - x - 1)/((x + 1)*(x^2 + 1)*(x^4 + 1)*(x^3 + x^2 + x - 1)). (End)

%t g[x_] = (x - 1)^2/(-4*x) M = {{0, 1, 0}, {0, 0, 1}, {1, 1, 1}} w[0] = {0, 1, 1}; w[n_] := w[n] = M.w[n - 1] a0 = Table[ -Floor[g[w[n][[1]]]], {n, 1, 25}] b0 = Table[N[a0[[n + 1]]/a0[[n]]], {n, 2, 24}]

%Y Cf. A000073.

%K nonn,uned

%O 2,5

%A _Roger L. Bagula_, Mar 13 2006