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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)*.
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%I #17 Mar 05 2019 01:43:27

%S 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 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 55,21,54,23,8,13,10,9,6,3,156,25,55,11

%N 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 Rows are ultimately periodic.

%H Charlie Neder, <a href="/A306640/b306640.txt">First 45 antidiagonals, flattened</a>

%H Klaus Sutner and Sam Tetruashvili, <a href="http://www.cs.cmu.edu/~sutner/papers/auto-seq.pdf">Inferring Automatic Sequences</a>.

%F A(n,n^k) = Sum_{i=0..k} n^i.

%F A(n+1,n) = n.

%F It also appears that A(n-1,n) = 2n.

%e Array begins:

%e 3 2 3 2 3

%e 6 4 3 6 4

%e 7 8 5 4 9 ...

%e 20 20 10 6 5

%e 13 7 7 12 7

%e ...

%Y Columns: A217519-A217521 (n = 2-4), A247566-A247581 (n = 5-20).

%Y Rows: A217515-A217518 (k = 3-6), A247387-A247391 (k = 7-11), A247434-A247442 (k = 12-20).

%K nonn,tabl

%O 1,1

%A _Charlie Neder_, Mar 02 2019