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A306640 Array read by antidiagonals: A(n,k) (n,k >= 2) is the base-n state complexity of the partitioned finite deterministic automaton (PFDA) for the periodic sequence (123..k)*.

%I A306640 #17 Mar 05 2019 01:43:27
%S A306640 3,6,2,7,4,3,20,8,3,2,13,20,5,6,3,21,7,10,4,4,2,15,42,7,6,9,3,3,54,16,
%T A306640 21,12,5,8,6,2,41,13,13,42,7,20,5,4,3,110,40,27,16,14,6,20,4,3,2,27,
%U A306640 55,21,54,23,8,13,10,9,6,3,156,25,55,11
%N A306640 Array read by antidiagonals: A(n,k) (n,k >= 2) is the base-n state complexity of the partitioned finite deterministic automaton (PFDA) for the periodic sequence (123..k)*.
%C A306640 Rows are ultimately periodic.
%H A306640 Charlie Neder, <a href="/A306640/b306640.txt">First 45 antidiagonals, flattened</a>
%H A306640 Klaus Sutner and Sam Tetruashvili, <a href="http://www.cs.cmu.edu/~sutner/papers/auto-seq.pdf">Inferring Automatic Sequences</a>.
%F A306640 A(n,n^k) = Sum_{i=0..k} n^i.
%F A306640 A(n+1,n) = n.
%F A306640 It also appears that A(n-1,n) = 2n.
%e A306640 Array begins:
%e A306640    3   2   3   2   3
%e A306640    6   4   3   6   4
%e A306640    7   8   5   4   9  ...
%e A306640   20  20  10   6   5
%e A306640   13   7   7  12   7
%e A306640           ...
%Y A306640 Columns: A217519-A217521 (n = 2-4), A247566-A247581 (n = 5-20).
%Y A306640 Rows: A217515-A217518 (k = 3-6), A247387-A247391 (k = 7-11), A247434-A247442 (k = 12-20).
%K A306640 nonn,tabl
%O A306640 1,1
%A A306640 _Charlie Neder_, Mar 02 2019