A247435 - OEIS

%I #11 Sep 08 2022 08:46:09

%S 156,39,78,52,156,156,52,39,78,156,26,14,13,156,39,78,52,156,156,52,

%T 39,78,156,26,14,13,156,39,78,52,156,156,52,39,78,156,26,14,13,156,39,

%U 78,52,156,156,52,39,78,156,26,14,13,156,39,78,52,156,156,52,39

%N Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123....13)*

%H 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 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,1).

%F G.f.: x^2*(156 + 39*x + 78*x^2 + 52*x^3 + 156*x^4 + 156*x^5 + 52*x^6 + 39*x^7 + 78*x^8 + 156*x^9 + 26*x^10 + 14*x^11 + 13*x^12)/(1 - x^13).

%t CoefficientList[Series[(156 + 39 x + 78 x^2 + 52 x^3 + 156 x^4 + 156 x^5 + 52 x^6 + 39 x^7 + 78 x^8 + 156 x^9 + 26 x^10 + 14 x^11 + 13 x^12)/(1 - x^13), {x, 0, 60}], x]

%t PadRight[{},120,{156,39,78,52,156,156,52,39,78,156,26,14,13}] (* _Harvey P. Dale_, Mar 19 2021 *)

%o (Magma) &cat[[156, 39, 78, 52, 156, 156, 52, 39, 78, 156, 26, 14, 13]: n in [0..10]];

%Y Cf. A176059, A217515 - A217518, A247387, A247389 - A247391.

%K nonn,easy

%O 2,1

%A _Vincenzo Librandi_, Sep 19 2014