%I #19 Sep 08 2022 08:46:04

%S 13,7,7,12,7,6,13,7,7,12,7,6,13,7,7,12,7,6,13,7,7,12,7,6,13,7,7,12,7,

%T 6,13,7,7,12,7,6,13,7,7,12,7,6,13,7,7,12,7,6,13,7,7,12,7,6,13,7,7,12,

%U 7,6,13,7,7,12,7,6,13,7,7,12,7,6,13

%N Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123456)*.

%H Klaus Sutner and Sam Tetruashvili, <a href="http://www.cs.cmu.edu/~sutner/papers/auto-seq.pdf ">Inferring automatic sequences</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1).

%F Periodic with period length 6.

%F G.f.: x^2(13 + 7*x + 7*x^2 + 12x^3 + 7x^4 + 6x^5)/((1 - x^6)). - _Vincenzo Librandi_, Nov 18 2012

%t CoefficientList[Series[(13 + 7*x + 7*x^2 + 12x^3 + 7x^4 + 6x^5)/((1 - x^6)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 18 2012 *)

%t LinearRecurrence[{0,0,0,0,0,1},{13,7,7,12,7,6},80] (* or *) PadRight[ {},80,{13,7,7,12,7,6}] (* _Harvey P. Dale_, Jul 19 2016 *)

%o (Magma) &cat[[13, 7, 7, 12, 7, 6]: n in [0..30]]; // _Vincenzo Librandi_, Nov 18 2012

%o (PARI) a(n)=[7, 6, 13, 7, 7, 12][n%6+1] \\ _Charles R Greathouse IV_, Nov 18 2012

%K nonn,easy

%O 2,1

%A _N. J. A. Sloane_, Oct 07 2012