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%I #27 Jul 13 2023 09:50:48
%S 8,57,406,2891,20585,146572,1043641,7431068,52911654,376748420,
%T 2682572954,19100803803,136004020087,968393459804,6895280686492,
%U 49096671672207,349584488128334,2489156803863966,17723617050044085,126197996385357735,898571338272012057
%N Define the sequence T(a_0,a_1) by a_{n+2} is the greatest integer such that a_{n+2}/a_{n+1}<a_{n+1}/a_n for n >= 0. This is T(8,57).
%H Alois P. Heinz, <a href="/A022038/b022038.txt">Table of n, a(n) for n = 0..1171</a>
%H D. W. Boyd, <a href="http://www.researchgate.net/publication/258834801">Linear recurrence relations for some generalized Pisot sequences</a>, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993.
%H <a href="/index/Ph#Pisot">Index entries for Pisot sequences</a>
%p a:= proc(n) option remember;
%p `if`(n<2, [8, 57][n+1], ceil(a(n-1)^2/a(n-2))-1)
%p end:
%p seq(a(n), n=0..30); # _Alois P. Heinz_, Sep 18 2015
%t a[n_] := a[n] = Switch[n, 0, 8, 1, 57, _, Ceiling[a[n-1]^2/a[n-2]] - 1];
%t a /@ Range[0, 30] (* _Jean-François Alcover_, Nov 16 2020, after _Alois P. Heinz_ *)
%o (PARI) T(a0, a1, maxn) = a=vector(maxn); a[1]=a0; a[2]=a1; for(n=3, maxn, a[n]=ceil(a[n-1]^2/a[n-2])-1); a
%o T(8, 57, 30) \\ _Colin Barker_, Feb 14 2016
%K nonn
%O 0,1
%A _R. K. Guy_
%E Incorrect g.f. deleted by _Alois P. Heinz_, Sep 18 2015
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