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A250253 First row of spectral array W(gamma+1).

%I A250253 #10 Nov 16 2014 12:43:23
%S A250253 1,2,3,5,7,13,20,35,55,95,149,259,408,707,1115,1931,3045,5276,8321,
%T A250253 14416,22737,39391,62128,107634,169762,294105,463867,803628,1267494,
%U A250253 2195877,3463371,6000134,9463505,16395094
%N A250253 First row of spectral array W(gamma+1).
%C A250253 Gamma is Euler's (or Euler-Mascheroni) constant.
%H A250253 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 A250253 (PARI)
%o A250253 \\ Row i of the generalized Wythoff array W(h),
%o A250253 \\   where h is an irrational number between 1 and 2,
%o A250253 \\   and m is the number of terms in the vectors a and b.
%o A250253 row(h, i, m) = {
%o A250253   if(h<=1 || h>=2, print("Invalid value for h"); return);
%o A250253   my(
%o A250253     a=vector(m, n, floor(n*h)),
%o A250253     b=vector(m, n, floor(n*h/(h-1))),
%o A250253     w=[a[a[i]], b[a[i]]],
%o A250253     j=3
%o A250253   );
%o A250253   while(1,
%o A250253     if(j%2==1,
%o A250253       if(w[j-1]<=#a, w=concat(w, a[w[j-1]]), return(w))
%o A250253     ,
%o A250253       if(w[j-2]<=#b, w=concat(w, b[w[j-2]]), return(w))
%o A250253     );
%o A250253     j++
%o A250253   )
%o A250253 }
%o A250253 allocatemem(10^9)
%o A250253 row(Euler+1, 1, 10^7)
%Y A250253 Cf. A001620 (Gamma), A059555 (Corresponding Beatty sequence), A250254, A250255.
%K A250253 nonn,more
%O A250253 1,2
%A A250253 _Colin Barker_, Nov 15 2014