A247435 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123....13)*.
156, 39, 78, 52, 156, 156, 52, 39, 78, 156, 26, 14, 13, 156, 39, 78, 52, 156, 156, 52, 39, 78, 156, 26, 14, 13, 156, 39, 78, 52, 156, 156, 52, 39, 78, 156, 26, 14, 13, 156, 39, 78, 52, 156, 156, 52, 39, 78, 156, 26, 14, 13, 156, 39, 78, 52, 156, 156, 52, 39
Offset: 2
Links
- Klaus Sutner and Sam Tetruashvili, Inferring automatic sequences (see table on the p. 5).
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,1).
Programs
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Magma
&cat[[156, 39, 78, 52, 156, 156, 52, 39, 78, 156, 26, 14, 13]: n in [0..10]];
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Mathematica
CoefficientList[Series[(156 + 39 x + 78 x^2 + 52 x^3 + 156 x^4 + 156 x^5 + 52 x^6 + 39 x^7 + 78 x^8 + 156 x^9 + 26 x^10 + 14 x^11 + 13 x^12)/(1 - x^13), {x, 0, 60}], x] PadRight[{},120,{156,39,78,52,156,156,52,39,78,156,26,14,13}] (* Harvey P. Dale, Mar 19 2021 *)
Formula
G.f.: x^2*(156 + 39*x + 78*x^2 + 52*x^3 + 156*x^4 + 156*x^5 + 52*x^6 + 39*x^7 + 78*x^8 + 156*x^9 + 26*x^10 + 14*x^11 + 13*x^12)/(1 - x^13).