A217518 -id:A217518 - cp's OEIS frontend

A247387 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (1234567)*.

21, 42, 21, 42, 14, 8, 7, 21, 42, 21, 42, 14, 8, 7, 21, 42, 21, 42, 14, 8, 7, 21, 42, 21, 42, 14, 8, 7, 21, 42, 21, 42, 14, 8, 7, 21, 42, 21, 42, 14, 8, 7, 21, 42, 21, 42, 14, 8, 7, 21, 42, 21, 42, 14, 8, 7, 21, 42, 21, 42, 14, 8, 7, 21, 42, 21, 42, 14, 8, 7

Offset: 2

Vincenzo Librandi, Sep 16 2014

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

Cf. A176059, A217515, A217516, A217517, A217518.

&cat[[21, 42, 21, 42, 14, 8,7]: n in [0..30]];

CoefficientList[Series[(21 + 42 x + 21 x^2 + 42 x^3 + 14 x^4 + 8 x^5 + 7 x^6)/(1 - x^7), {x, 0, 40}], x]

G.f.: x^2*(21 + 42*x + 21*x^2 + 42*x^3 + 14*x^4 + 8*x^5 + 7*x^6)/(1-x^7).

A247391 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (1234567891011).

Original entry on oeis.org

110, 55, 55, 55, 110, 110, 110, 55, 22, 12, 11, 110, 55, 55, 55, 110, 110, 110, 55, 22, 12, 11, 110, 55, 55, 55, 110, 110, 110, 55, 22, 12, 11, 110, 55, 55, 55, 110, 110, 110, 55, 22, 12, 11, 110, 55, 55, 55, 110, 110, 110, 55, 22, 12, 11, 110, 55, 55, 55

Offset: 2

Vincenzo Librandi, Sep 17 2014

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

Cf. A176059, A217515, A217516, A217517, A217518, A247387, A247390.

Cf. A010880.

&cat[[110,55,55,55,110,110,110,55,22,12,11]: n in [0..10]];

CoefficientList[Series[(110 + 55 x + 55 x^2 + 55 x^3 + 110 x^4 + 110 x^5 + 110 x^6 + 55 x^7 + 22 x^8 + 12 x^9 + 11 x^10)/(1-x^11), {x, 0, 60}], x]

G.f.: x^2*(110 + 55*x + 55*x^2 + 55*x^3 + 110*x^4 + 110*x^5 + 110*x^6 + 55*x^7 + 22*x^8 + 12*x^9 + 11*x^10)/(1-x^11).

a(n) = (1283*m^10 - 64570*m^9 + 1396065*m^8 - 16960020*m^7 + 127065939*m^6 - 605936100*m^5 + 1828078285*m^4 - 3335483030*m^3 + 3289569228*m^2 - 1288120680*m + 5443200)/453600 where m = (n mod 11). - Luce ETIENNE, Nov 04 2018

A247390 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (12345678910)*.

Original entry on oeis.org

41, 40, 21, 11, 11, 40, 41, 20, 11, 10, 41, 40, 21, 11, 11, 40, 41, 20, 11, 10, 41, 40, 21, 11, 11, 40, 41, 20, 11, 10, 41, 40, 21, 11, 11, 40, 41, 20, 11, 10, 41, 40, 21, 11, 11, 40, 41, 20, 11, 10, 41, 40, 21, 11, 11, 40, 41, 20, 11, 10, 41, 40, 21, 11, 11, 40

Offset: 2

Vincenzo Librandi, Sep 16 2014

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

Cf. A176059, A217515 - A217518, A247387.

&cat[[41,40,21,11,11,40,41,20,11,10]: n in [0..10]];

CoefficientList[Series [(41 + 40 x + 21 x^2 + 11 x^3 + 11 x^4 + 40 x^5 + 41 x^6 + 20 x^7 + 11 x^8 + 10 x^9)/(1 - x^10), {x, 0, 40}], x]

G.f.: x^2*(41 + 40*x + 21*x^2 + 11*x^3 + 11*x^4 + 40*x^5 + 41*x^6 + 20*x^7 + 11*x^8 + 10*x^9) / (1-x^10).

A247389 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123456789)*.

Original entry on oeis.org

54, 13, 27, 54, 16, 27, 18, 10, 9, 54, 19, 27, 54, 19, 27, 18, 10, 9, 54

Offset: 2

Vincenzo Librandi, Sep 16 2014

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

Cf. A176059, A217515 - A217518, A247387.

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.

A247388 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (12345678)*.

Original entry on oeis.org

15, 16, 13, 16, 23, 16, 9, 8, 25, 16, 17, 16, 25, 16, 9, 8, 25, 16, 17

Offset: 2

Vincenzo Librandi, Sep 16 2014

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

Cf. A176059, A217515 - A217518, A247387.

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) ).

cp's OEIS Frontend

A247387 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (1234567)*.

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A247391 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (1234567891011).

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A247390 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (12345678910)*.

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A247389 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123456789)*.

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

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

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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)*.

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A247388 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (12345678)*.

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Keywords

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

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Magma

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

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