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%I #13 Sep 08 2022 08:45:56
%S 4,7,1,2,2,1,4,4,5,0,4,4,9,0,2,6,1,8,0,4,3,6,5,5,2,8,5,3,7,2,9,4,0,6,
%T 1,2,0,4,2,4,0,3,4,0,7,1,8,6,0,6,9,1,0,4,2,9,3,0,7,8,8,6,3,2,4,5,9,1,
%U 1,0,1,4,5,9,2,6,9,1,9,6,5,7,5,2,3,3,0,0,1,9,6,0,2,8,8,5,6,4,4,0,6,0,9,5,2,5,2,9,9,7,1,7,9,3,7,2,9,9,9,2,9,5,1,8,7,7,5,9,3,4
%N Decimal expansion of (9+sqrt(97))/4.
%C Decimal expansion of the length/width ratio of a (9/2)-extension rectangle. See A188640 for definitions of shape and r-extension rectangle.
%C A (9/2)-extension rectangle matches the continued fraction [4,1,2,2,9,2,2,1,4,4,1,2,2,9,...] for the shape L/W=(9+sqrt(97))/4. This is analogous to the matching of a golden rectangle to the continued fraction [1,1,1,1,1,1,1,1,...]. Specifically, for the (9/2)-extension rectangle, 4 squares are removed first, then 1 square, then 2 squares, then 2 squares,..., so that the original rectangle of shape (9+sqrt(97))/4 is partitioned into an infinite collection of squares.
%H G. C. Greubel, <a href="/A188735/b188735.txt">Table of n, a(n) for n = 1..10000</a>
%e 4.712214450449026180436552853729406120424034071860691042930...
%p evalf((9+sqrt(97))/4,140); # _Muniru A Asiru_, Nov 01 2018
%t r = 9/2; t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]
%t N[t, 130]
%t RealDigits[N[t, 130]][[1]]
%t ContinuedFraction[t, 120]
%o (PARI) (sqrt(97)+9)/4 \\ _Charles R Greathouse IV_, Apr 25 2016
%o (Magma) SetDefaultRealField(RealField(100)); (9+Sqrt(97))/4; // _G. C. Greubel_, Nov 01 2018
%Y Cf. A188640, A188734.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Apr 12 2011
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