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%I #15 Jan 31 2023 16:54:58
%S 4,2,6,5,5,6,4,4,3,7,0,7,4,6,3,7,4,1,3,0,9,1,6,5,3,3,0,7,5,7,5,9,4,2,
%T 7,8,2,7,8,3,5,9,9,0,7,6,4,0,2,1,4,3,3,4,6,9,8,4,1,4,8,0,9,7,3,1,5,9,
%U 6,8,7,3,7,7,5,6,4,2,2,0,5,0,7,4,0,0,3,8,5,6,6,6,7,9,3,0,7,6,6,0,9,0,9,3,6,0,6,1,6,5,3,4,9,8,6,4,7,8,0,5,3,4,3,7,1,6,3,0,3,0
%N Decimal expansion of (9+sqrt(65))/4.
%C Apart from the first digit, the same as A171417. Apart from the first 2 digits, the same as A188734. - _R. J. Mathar_, Apr 15 2011
%C Decimal expansion of the shape (= length/width = (9+sqrt(65))/4) of the greater (9/2)-contraction rectangle.
%C See A188738 for an introduction to lesser and greater r-contraction rectangles, their shapes, and partitioning these rectangles into a sets of squares in a manner that matches the continued fractions of their shapes.
%e 4.2655644370746374130916533075759427827835990...
%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 RealDigits[(9+Sqrt[65])/4,10,150][[1]] (* _Harvey P. Dale_, Jan 31 2023 *)
%o (PARI) (9+sqrt(65))/4 \\ _Jinyuan Wang_, Apr 14 2020
%Y Cf. A188738, A188940.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Apr 14 2011
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