A247391 -id:A247391 - cp's OEIS frontend

A247434 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123.....12)*.

Original entry on oeis.org

27, 25, 13, 24, 19, 24, 25, 13, 23, 24, 13, 12, 37, 25, 13, 24, 25, 24, 25

Offset: 2

Vincenzo Librandi, Sep 19 2014

Klaus Sutner and Sam Tetruashvili, Inferring automatic sequences (see table on the p. 5).

Cf. A176059, A217515 - A217518, A247387, A247390, A247391.

A247442 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...20)*.

Original entry on oeis.org

83, 80, 41, 21, 27, 80, 81, 40, 31, 40, 81, 80, 55, 41, 21, 80, 99, 40, 21

Offset: 2

Vincenzo Librandi, Sep 20 2014

Klaus Sutner and Sam Tetruashvili, Inferring automatic sequences (see table on the p. 5).

Cf. A176059, A217515 - A217518, A247387, A247390, A247391.

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)*.

Original entry on oeis.org

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

Charlie Neder, Mar 02 2019

Rows are ultimately periodic.

			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
          ...

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

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).

A(n,n^k) = Sum_{i=0..k} n^i.
A(n+1,n) = n.
It also appears that A(n-1,n) = 2n.

A247435 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123....13)*.

Original entry on oeis.org

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

Vincenzo Librandi, Sep 19 2014

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).

Cf. A176059, A217515 - A217518, A247387, A247389 - A247391.

&cat[[156, 39, 78, 52, 156, 156, 52, 39, 78, 156, 26, 14, 13]: n in [0..10]];

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 *)

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).

A247436 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...14)*.

Original entry on oeis.org

43, 84, 43, 84, 29, 15, 15, 42, 85, 42, 85, 28, 15, 14, 43, 84, 43, 84, 29, 15, 15, 42, 85, 42, 85, 28, 15, 14, 43, 84, 43, 84, 29, 15, 15, 42, 85, 42, 85, 28, 15, 14, 43, 84, 43, 84, 29, 15, 15, 42, 85, 42, 85, 28, 15, 14, 43, 84, 43, 84, 29, 15, 15, 42

Offset: 2

Vincenzo Librandi, Sep 19 2014

Period 14, repeat [43, 84, 43, 84, 29, 15, 15, 42, 85, 42, 85, 28, 15, 14].

Klaus Sutner and Sam Tetruashvili, Inferring automatic sequences (see table on the p. 5).
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Cf. A176059, A217515 - A217518, A247387 - A247391.

&cat[[43, 84, 43, 84, 29, 15, 15, 42, 85, 42, 85, 28, 15, 14]: n in [0..10]];

CoefficientList[Series[(43 + 84 x + 43 x^2 + 84 x^3 + 29 x^4 + 15 x^5 + 15 x^6 + 42 x^7 + 85 x^8 + 42 x^9 + 85 x^10 + 28 x^11 + 15 x^12 + 14 x^13)/(1 - x^14), {x, 0, 60}], x]

G.f.: -x^2*(43+84*x+43*x^2+84*x^3+29*x^4+15*x^5+15*x^6+42*x^7+85*x^8+42*x^9+85
*x^10+28*x^11+15*x^12+14*x^13) / ( (x-1)*(1+x^6+x^5+x^4+x^3+x^2+x)*(1+x)*(1-x+
x^2-x^3+x^4-x^5+x^6) ).

A247437 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...15)*.

Original entry on oeis.org

60, 61, 30, 31, 16, 60, 60, 31, 16, 30, 61, 60, 30, 16, 15, 60, 61, 30, 31

Offset: 2

Vincenzo Librandi, Sep 20 2014

Klaus Sutner and Sam Tetruashvili, Inferring automatic sequences (see table on the p. 5).

Cf. A176059, A217515 - A217518, A247387, A247390, A247391.

A247438 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...16)*.

Original entry on oeis.org

31, 64, 21, 64, 55, 32, 25, 32, 59, 64, 29, 64, 63, 32, 17, 16, 65, 64, 33

Offset: 2

Vincenzo Librandi, Sep 20 2014

Klaus Sutner and Sam Tetruashvili, Inferring automatic sequences (see table on the p. 5).

Cf. A176059, A217515 - A217518, A247387, A247390, A247391.

A247439 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...17)*.

Original entry on oeis.org

136, 272, 68, 272, 272, 272, 136, 136, 272, 272, 272, 68, 272, 136, 34, 18, 17, 136, 272

Offset: 2

Vincenzo Librandi, Sep 20 2014

Klaus Sutner and Sam Tetruashvili, Inferring automatic sequences (see table on the p. 5).

Cf. A176059, A217515 - A217518, A247387, A247390, A247391.

A247440 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...18)*.

Original entry on oeis.org

109, 22, 55, 108, 25, 54, 37, 19, 19, 108, 31, 54, 109, 34, 55, 36, 19, 18, 109

Offset: 2

Vincenzo Librandi, Sep 20 2014

Klaus Sutner and Sam Tetruashvili, Inferring automatic sequences (see table on the p. 5).

Cf. A176059, A217515 - A217518, A247387, A247390, A247391.

A247441 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...19)*.

Original entry on oeis.org

342, 342, 171, 171, 171, 57, 114, 171, 342, 57, 114, 342, 342, 342, 171, 171, 38, 20, 19

Offset: 2

Vincenzo Librandi, Sep 20 2014

Klaus Sutner and Sam Tetruashvili, Inferring automatic sequences (see table on the p. 5).

Cf. A176059, A217515 - A217518, A247387, A247390, A247391.

cp's OEIS Frontend

A247434 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123.....12)*.

Views

Author

Keywords

Links

Crossrefs

A247442 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...20)*.

Views

Author

Keywords

Links

Crossrefs

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)*.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A247435 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123....13)*.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

Formula

A247436 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...14)*.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

Formula

A247437 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...15)*.

Views

Author

Keywords

Links

Crossrefs

A247438 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...16)*.

Views

Author

Keywords

Links

Crossrefs

A247439 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...17)*.

Views

Author

Keywords

Links

Crossrefs

A247440 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...18)*.

Views

Author

Keywords

Links

Crossrefs

A247441 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...19)*.

Views

Author

Keywords

Links

Crossrefs