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

2,1

Links

Table of n, a(n) for n=2..60.

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).

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

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]

Prog

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

Crossrefs

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

Cf. A010880.

Sequence in context: A087303 A336740 A045884 * A110736 A084292 A266849

Adjacent sequences: A247388 A247389 A247390 * A247392 A247393 A247394

Keyword

nonn,easy

Author

Vincenzo Librandi, Sep 17 2014

Status

approved