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)*.

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

Offset: 1

Author

Charlie Neder, Mar 02 2019

Keywords

• nonn
• tabl

Comments

Rows are ultimately periodic.

Examples

			Array begins:
   3   2   3   2   3
   6   4   3   6   4
   7   8   5   4   9  ...
  20  20  10   6   5
  13   7   7  12   7
          ...
		

Links

• Charlie Neder, First 45 antidiagonals, flattened
• Klaus Sutner and Sam Tetruashvili, Inferring Automatic Sequences.

Crossrefs

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

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

Formula

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

A(n+1,n) = n.

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