A217518 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123456)*.

13, 7, 7, 12, 7, 6, 13, 7, 7, 12, 7, 6, 13, 7, 7, 12, 7, 6, 13, 7, 7, 12, 7, 6, 13, 7, 7, 12, 7, 6, 13, 7, 7, 12, 7, 6, 13, 7, 7, 12, 7, 6, 13, 7, 7, 12, 7, 6, 13, 7, 7, 12, 7, 6, 13, 7, 7, 12, 7, 6, 13, 7, 7, 12, 7, 6, 13, 7, 7, 12, 7, 6, 13

Offset: 2

Author

N. J. A. Sloane, Oct 07 2012

Keywords

• nonn
• easy

Links

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

Programs

Magma

&cat[[13, 7, 7, 12, 7, 6]: n in [0..30]]; // Vincenzo Librandi, Nov 18 2012

Mathematica

CoefficientList[Series[(13 + 7*x + 7*x^2 + 12x^3 + 7x^4 + 6x^5)/((1 - x^6)), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 18 2012 *)
LinearRecurrence[{0,0,0,0,0,1},{13,7,7,12,7,6},80] (* or *) PadRight[ {},80,{13,7,7,12,7,6}] (* Harvey P. Dale, Jul 19 2016 *)

PARI

a(n)=[7, 6, 13, 7, 7, 12][n%6+1] \\ Charles R Greathouse IV, Nov 18 2012

Formula

Periodic with period length 6.

G.f.: x^2(13 + 7*x + 7*x^2 + 12x^3 + 7x^4 + 6x^5)/((1 - x^6)). - Vincenzo Librandi, Nov 18 2012