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A247436 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...14)*.

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%I A247436 #13 Jul 23 2025 11:34:46
%S A247436 43,84,43,84,29,15,15,42,85,42,85,28,15,14,43,84,43,84,29,15,15,42,85,
%T A247436 42,85,28,15,14,43,84,43,84,29,15,15,42,85,42,85,28,15,14,43,84,43,84,
%U A247436 29,15,15,42,85,42,85,28,15,14,43,84,43,84,29,15,15,42
%N A247436 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...14)*.
%C A247436 Period 14, repeat [43, 84, 43, 84, 29, 15, 15, 42, 85, 42, 85, 28, 15, 14].
%H A247436 Klaus Sutner and Sam Tetruashvili, <a href="http://www.cs.cmu.edu/~sutner/papers/auto-seq.pdf">Inferring automatic sequences</a>  (see table on the p. 5).
%H A247436 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,1).
%F A247436 G.f.: -x^2*(43+84*x+43*x^2+84*x^3+29*x^4+15*x^5+15*x^6+42*x^7+85*x^8+42*x^9+85
%F A247436 *x^10+28*x^11+15*x^12+14*x^13) / ( (x-1)*(1+x^6+x^5+x^4+x^3+x^2+x)*(1+x)*(1-x+
%F A247436 x^2-x^3+x^4-x^5+x^6) ).
%t A247436 CoefficientList[Series[(43 + 84 x + 43 x^2 + 84 x^3 + 29 x^4 + 15 x^5 + 15 x^6 + 42 x^7 + 85 x^8 + 42 x^9 + 85 x^10 + 28 x^11 + 15 x^12 + 14 x^13)/(1 - x^14), {x, 0, 60}], x]
%o A247436 (Magma) &cat[[43, 84, 43, 84, 29, 15, 15, 42, 85, 42, 85, 28, 15, 14]: n in [0..10]];
%Y A247436 Cf. A176059, A217515 - A217518, A247387 - A247391.
%K A247436 nonn,easy
%O A247436 2,1
%A A247436 _Vincenzo Librandi_, Sep 19 2014