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A249179 First row of spectral array W(3^(1/3)).

%I A249179 #26 Dec 14 2014 02:50:00
%S A249179 1,3,4,9,12,29,41,94,135,306,441,997,1437,3251,4688,10602,15290,34574,
%T A249179 49864,112751,162615,367699,530313,1199127,1729440,3910553,5639993,
%U A249179 12752965
%N A249179 First row of spectral array W(3^(1/3)).
%C A249179 3^(1/3) = 1.442249570307408382321638310780109588391869253499350577546416...
%C A249179 The sequence is generated from the Beatty sequence (A059539) and from the complement of the Beatty sequence (A059540) for 3^(1/3).
%H A249179 A. Fraenkel and C. Kimberling, <a href="http://dx.doi.org/10.1016/0012-365X(94)90259-3">Generalized Wythoff arrays, shuffles and interspersions</a>, Discrete Mathematics 126 (1994) 137-149.
%o A249179 (PARI)
%o A249179 \\ Row i of the generalized Wythoff array W(h),
%o A249179 \\   where h is an irrational number between 1 and 2,
%o A249179 \\   and m is the number of terms in the vectors b and c.
%o A249179 row(h, i, m) = {
%o A249179   if(h<=1 || h>=2, print("Invalid value for h"); return);
%o A249179   my(
%o A249179     b=vector(m, n, floor(n*h)),       \\ Beatty sequence for h
%o A249179     c=vector(m, n, floor(n*h/(h-1))), \\ Complement of b
%o A249179     w=[b[b[i]], c[b[i]]],
%o A249179     j=3
%o A249179   );
%o A249179   while(1,
%o A249179     if(j%2==1,
%o A249179       if(w[j-1]<=#b, w=concat(w, b[w[j-1]]), return(w))
%o A249179     ,
%o A249179       if(w[j-2]<=#c, w=concat(w, c[w[j-2]]), return(w))
%o A249179     );
%o A249179     j++
%o A249179   )
%o A249179 }
%o A249179 allocatemem(10^9)
%o A249179 default(realprecision, 100)
%o A249179 row(3^(1/3), 1, 10^7)
%Y A249179 Cf. A059539, A059540.
%K A249179 nonn,more
%O A249179 1,2
%A A249179 _Colin Barker_, Dec 03 2014