A247391 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (1234567891011).

110, 55, 55, 55, 110, 110, 110, 55, 22, 12, 11, 110, 55, 55, 55, 110, 110, 110, 55, 22, 12, 11, 110, 55, 55, 55, 110, 110, 110, 55, 22, 12, 11, 110, 55, 55, 55, 110, 110, 110, 55, 22, 12, 11, 110, 55, 55, 55, 110, 110, 110, 55, 22, 12, 11, 110, 55, 55, 55

Offset: 2

Author

Vincenzo Librandi, Sep 17 2014

Keywords

• nonn
• easy

Links

• Klaus Sutner and Sam Tetruashvili, Inferring automatic sequences (see table on the p. 5).
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,1).

Crossrefs

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

Cf. A010880.

Programs

Magma

&cat[[110,55,55,55,110,110,110,55,22,12,11]: n in [0..10]];

Mathematica

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]

Formula

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).

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