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%I #15 Jan 14 2018 00:06:09
%S 3,5,11,19,41,71,153,265,571,989,2131,3691,7953,13775,29681,51409,
%T 110771,191861,413403,716035,1542841,2672279,5757961,9973081,21489003,
%U 37220045,80198051,138907099,299303201,518408351,1117014753,1934726305,4168755811,7220496869,15558008491,26947261171
%N Number of Khalimsky-continuous functions with a three-point codomain.
%H Neo Scott, <a href="/A131887/b131887.txt">Table of n, a(n) for n = 1..1500</a>
%H Shiva Samieinia, <a href="http://www.math.su.se/reports/2007/6/">Digital straight line segments and curves</a>. Licentiate Thesis. Stockholm University, Department of Mathematics, Report 2007:6.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,0,-1).
%F a(2k) = a(2k-1) + a(2k-2) + a(2k-3) and a(2k-1) = a(2k-2) + 2a(2k-3).
%F The asymptotic behavior is a(2k) = t(2k) sqrt(3)(2 + sqrt(3))^k, a(2k-1) = t(2k-1)(2 + sqrt(3))^k where t(n) tends to 1/2 + sqrt(3)/6.
%F G.f.: -x*(-3-5*x+x^2+x^3) / ( 1-4*x^2+x^4 ). - _R. J. Mathar_, Nov 08 2013
%t LinearRecurrence[{0,4,0,-1},{3,5,11,19},40] (* _Harvey P. Dale_, Jan 01 2017 *)
%Y Cf. A001045, A000213, A131935, A001834 (bisection), A001835 (bisection)
%K nonn,easy
%O 1,1
%A Shiva Samieinia (shiva(AT)math.su.se), Oct 05 2007, Oct 09 2007
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