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

2,1

Links

Table of n, a(n) for n=2..74.

Klaus Sutner and Sam Tetruashvili, Inferring automatic sequences

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).

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

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 *)

Prog

(Magma) &cat[[13, 7, 7, 12, 7, 6]: n in [0..30]]; // Vincenzo Librandi, Nov 18 2012
(PARI) a(n)=[7, 6, 13, 7, 7, 12][n%6+1] \\ Charles R Greathouse IV, Nov 18 2012

Crossrefs

Sequence in context: A324279 A222464 A095389 * A364091 A257928 A206611

Adjacent sequences: A217515 A217516 A217517 * A217519 A217520 A217521

Keyword

nonn,easy

Author

N. J. A. Sloane, Oct 07 2012

Status

approved