A247436 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...14)*.

43, 84, 43, 84, 29, 15, 15, 42, 85, 42, 85, 28, 15, 14, 43, 84, 43, 84, 29, 15, 15, 42, 85, 42, 85, 28, 15, 14, 43, 84, 43, 84, 29, 15, 15, 42, 85, 42, 85, 28, 15, 14, 43, 84, 43, 84, 29, 15, 15, 42, 85, 42, 85, 28, 15, 14, 43, 84, 43, 84, 29, 15, 15, 42

Offset: 2

Author

Vincenzo Librandi, Sep 19 2014

Keywords

• nonn
• easy

Comments

Period 14, repeat [43, 84, 43, 84, 29, 15, 15, 42, 85, 42, 85, 28, 15, 14].

Links

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

Crossrefs

Cf. A176059, A217515 - A217518, A247387 - A247391.

Programs

Magma

&cat[[43, 84, 43, 84, 29, 15, 15, 42, 85, 42, 85, 28, 15, 14]: n in [0..10]];

Mathematica

CoefficientList[Series[(43 + 84 x + 43 x^2 + 84 x^3 + 29 x^4 + 15 x^5 + 15 x^6 + 42 x^7 + 85 x^8 + 42 x^9 + 85 x^10 + 28 x^11 + 15 x^12 + 14 x^13)/(1 - x^14), {x, 0, 60}], x]

Formula

G.f.: -x^2*(43+84*x+43*x^2+84*x^3+29*x^4+15*x^5+15*x^6+42*x^7+85*x^8+42*x^9+85

*x^10+28*x^11+15*x^12+14*x^13) / ( (x-1)*(1+x^6+x^5+x^4+x^3+x^2+x)*(1+x)*(1-x+

x^2-x^3+x^4-x^5+x^6) ).