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Continued fraction expansion of (29+sqrt(145))/12.
1

%I #18 Aug 07 2024 11:13:21

%S 3,2,2,1,1,1,2,2,1,1,1,2,2,1,1,1,2,2,1,1,1,2,2,1,1,1,2,2,1,1,1,2,2,1,

%T 1,1,2,2,1,1,1,2,2,1,1,1,2,2,1,1,1,2,2,1,1,1,2,2,1,1,1,2,2,1,1,1,2,2,

%U 1,1,1,2,2,1,1,1,2,2,1,1,1,2,2,1,1,1,2,2,1,1,1,2,2,1,1,1,2,2,1,1,1,2,2,1,1

%N Continued fraction expansion of (29+sqrt(145))/12.

%H I. Jensen, <a href="http://arXiv.org/abs/cond-mat/0008178">A transfer matrix approach to the enumeration of plane meanders</a>, arXiv:cond-mat/0008178 [cond-mat.stat-mech], 2000; J. Phys. A 33 (2000), no. 34, 5953-5963.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1).

%F From _Colin Barker_, Jan 10 2014: (Start)

%F a(n) = a(n-5) for n>5.

%F G.f.: (2*x^5-x^4-x^3-2*x^2-2*x-3) / ((x-1)*(x^4+x^3+x^2+x+1)). (End)

%e 3.420132881566024623344...

%t PadRight[{3},120,{1,2,2,1,1}] (* _Harvey P. Dale_, Oct 15 2015 *)

%Y Cf. A077451 (decimal expansion).

%K nonn,cofr,easy

%O 0,1

%A _N. J. A. Sloane_, Dec 01 2002

%E Offset changed by _Andrew Howroyd_, Aug 07 2024