login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A247391 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (1234567891011). 10

%I #22 Sep 08 2022 08:46:09

%S 110,55,55,55,110,110,110,55,22,12,11,110,55,55,55,110,110,110,55,22,

%T 12,11,110,55,55,55,110,110,110,55,22,12,11,110,55,55,55,110,110,110,

%U 55,22,12,11,110,55,55,55,110,110,110,55,22,12,11,110,55,55,55

%N Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (1234567891011).

%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_11">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,1).

%F G.f.: x^2*(110 + 55*x + 55*x^2 + 55*x^3 + 110*x^4 + 110*x^5 + 110*x^6 + 55*x^7 + 22*x^8 + 12*x^9 + 11*x^10)/(1-x^11).

%F a(n) = (1283*m^10 - 64570*m^9 + 1396065*m^8 - 16960020*m^7 + 127065939*m^6 - 605936100*m^5 + 1828078285*m^4 - 3335483030*m^3 + 3289569228*m^2 - 1288120680*m + 5443200)/453600 where m = (n mod 11). - _Luce ETIENNE_, Nov 04 2018

%t CoefficientList[Series[(110 + 55 x + 55 x^2 + 55 x^3 + 110 x^4 + 110 x^5 + 110 x^6 + 55 x^7 + 22 x^8 + 12 x^9 + 11 x^10)/(1-x^11), {x, 0, 60}], x]

%o (Magma) &cat[[110,55,55,55,110,110,110,55,22,12,11]: n in [0..10]];

%Y Cf. A176059, A217515, A217516, A217517, A217518, A247387, A247390.

%Y Cf. A010880.

%K nonn,easy

%O 2,1

%A _Vincenzo Librandi_, Sep 17 2014

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 07:20 EDT 2024. Contains 371235 sequences. (Running on oeis4.)