cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 10 results.

A207454 Number of 3 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.

Original entry on oeis.org

6, 36, 90, 330, 1008, 3354, 10710, 34884, 112530, 364722, 1179360, 3817938, 12352782, 39978180, 129366090, 418647162, 1354755024, 4384104618, 14187219750, 45910873476, 148570600866, 480784736226, 1555851810240, 5034842671650
Offset: 1

Views

Author

R. H. Hardin, Feb 17 2012

Keywords

Comments

Row 3 of A207453.

Examples

			Some solutions for n=5:
..0..1..0..1..1....1..1..1..1..0....1..0..1..0..1....1..0..1..1..1
..1..1..0..1..0....1..0..1..1..1....1..0..1..0..1....0..1..1..1..1
..0..1..0..1..0....1..0..1..0..0....1..0..1..0..1....0..1..0..1..0

Links

Crossrefs

Cf. A207453.

Formula

Empirical: a(n) = a(n-1) + 7*a(n-2) + 2*a(n-3) - 4*a(n-4).
Empirical g.f.: 6*x*(1 + 5*x + 2*x^2 - 4*x^3) / ((1 + x - x^2)*(1 - 2*x - 4*x^2)). - Colin Barker, Mar 05 2018

A207448 Number of n X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.

Original entry on oeis.org

2, 16, 90, 760, 5200, 46956, 370734, 3599104, 31807710, 329885620, 3198732768, 35206521816, 369188811082, 4287997640080, 48104913781890, 586813738039904, 6984278125524784, 89124296743065348, 1118012637781250310
Offset: 1

Views

Author

R. H. Hardin Feb 17 2012

Keywords

Comments

Diagonal of A207453

Examples

			Some solutions for n=5
..0..1..1..1..1....0..1..1..1..1....0..1..0..1..0....1..0..1..1..1
..0..1..0..1..1....0..1..0..1..0....1..1..0..1..0....1..0..1..1..1
..0..1..0..1..0....0..1..0..1..0....0..1..0..1..0....1..0..1..0..0
..0..1..0..1..0....0..1..0..1..0....0..1..0..1..0....1..0..1..0..0
..0..1..0..1..0....0..1..0..1..0....0..1..0..1..0....1..0..1..0..0

Links

A207449 Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.

Original entry on oeis.org

10, 100, 330, 760, 1450, 2460, 3850, 5680, 8010, 10900, 14410, 18600, 23530, 29260, 35850, 43360, 51850, 61380, 72010, 83800, 96810, 111100, 126730, 143760, 162250, 182260, 203850, 227080, 252010, 278700, 307210, 337600, 369930, 404260, 440650
Offset: 1

Views

Author

R. H. Hardin, Feb 17 2012

Keywords

Comments

Column 4 of A207453.

Examples

			Some solutions for n=5:
..1..0..1..0....1..0..1..0....1..1..1..0....0..1..1..0....1..1..0..0
..1..0..1..1....1..1..1..1....0..1..1..1....1..1..0..1....1..0..1..0
..1..0..1..1....0..1..0..1....0..1..0..0....1..1..0..0....1..0..1..0
..1..0..1..0....0..1..0..0....0..1..0..0....0..1..0..0....1..0..1..0
..1..0..1..0....0..1..0..0....0..1..0..0....0..1..0..0....1..0..1..0

Links

Crossrefs

Cf. A207453.

Formula

Empirical: a(n) = 10*n^3 + 10*n^2 - 10*n.
Conjectures from Colin Barker, Jun 22 2018: (Start)
G.f.: 10*x*(1 + 6*x - x^2) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
(End)

A207450 Number of n X 5 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.

Original entry on oeis.org

16, 256, 1008, 2560, 5200, 9216, 14896, 22528, 32400, 44800, 60016, 78336, 100048, 125440, 154800, 188416, 226576, 269568, 317680, 371200, 430416, 495616, 567088, 645120, 730000, 822016, 921456, 1028608, 1143760, 1267200, 1399216, 1540096
Offset: 1

Views

Author

R. H. Hardin, Feb 17 2012

Keywords

Comments

Column 5 of A207453.

Examples

			Some solutions for n=5:
  0 1 1 1 0      1 1 0 1 0      0 1 1 0 1      0 1 1 0 0
  1 0 1 0 1      0 1 1 0 1      1 1 0 1 1      0 1 0 1 1
  1 0 1 0 0      0 1 1 0 0      1 1 0 1 1      0 1 0 1 0
  1 0 1 0 0      0 1 1 0 0      1 1 0 1 1      0 1 0 1 0
  1 0 1 0 0      0 1 1 0 0      0 1 0 1 1      0 1 0 1 0

Links

Crossrefs

Cf. A207453.

Formula

Empirical: a(n) = 48*n^3 - 32*n^2.
Conjectures from Colin Barker, Jun 23 2018: (Start)
G.f.: 16*x*(1 + 12*x + 5*x^2) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
(End).

A207451 Number of n X 6 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.

Original entry on oeis.org

26, 676, 3354, 10088, 23530, 46956, 84266, 139984, 219258, 327860, 472186, 659256, 896714, 1192828, 1556490, 1997216, 2525146, 3151044, 3886298, 4742920, 5733546, 6871436, 8170474, 9645168, 11310650, 13182676, 15277626, 17612504, 20204938
Offset: 1

Views

Author

R. H. Hardin, Feb 17 2012

Keywords

Comments

Column 6 of A207453.

Examples

			Some solutions for n=5:
  1 0 1 0 1 1     0 1 1 0 1 0     1 1 1 0 1 0     1 1 0 1 1 0
  1 1 1 1 0 0     0 1 0 1 0 0     0 1 0 1 0 0     0 1 1 1 0 0
  0 1 1 1 0 0     0 1 0 1 0 0     0 1 0 1 0 0     0 1 1 1 0 0
  0 1 0 1 0 0     0 1 0 1 0 0     0 1 0 1 0 0     0 1 0 1 0 0
  0 1 0 1 0 0     0 1 0 1 0 0     0 1 0 1 0 0     0 1 0 1 0 0

Links

Crossrefs

Cf. A207453.

Formula

Empirical: a(n) = 26*n^4 + 78*n^3 - 104*n^2 + 26*n.
Conjectures from Colin Barker, Jun 23 2018: (Start)
G.f.: 26*x*(1 + 21*x + 9*x^2 - 7*x^3) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)

A207452 Number of n X 7 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.

Original entry on oeis.org

42, 1764, 10710, 36456, 92610, 196812, 370734, 640080, 1034586, 1588020, 2338182, 3326904, 4600050, 6207516, 8203230, 10645152, 13595274, 17119620, 21288246, 26175240, 31858722, 38420844, 45947790, 54529776, 64261050, 75239892, 87568614
Offset: 1

Views

Author

R. H. Hardin, Feb 17 2012

Keywords

Comments

Column 7 of A207453.

Examples

			Some solutions for n=5:
  0 1 1 0 1 1 1      0 1 1 1 1 1 1      0 1 0 1 0 1 1
  1 1 0 1 1 1 1      1 1 0 1 0 1 0      0 1 0 1 1 1 1
  0 1 0 1 0 1 1      1 1 0 1 0 1 0      0 1 0 1 0 1 1
  0 1 0 1 0 1 0      0 1 0 1 0 1 0      0 1 0 1 0 1 0
  0 1 0 1 0 1 0      0 1 0 1 0 1 0      0 1 0 1 0 1 0

Links

Crossrefs

Cf. A207453.

Formula

Empirical: a(n) = 168*n^4 - 84*n^3 - 84*n^2 + 42*n.
Conjectures from Colin Barker, Jun 23 2018: (Start)
G.f.: 42*x*(1 + 37*x + 55*x^2 + 3*x^3) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)

A207455 Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.

Original entry on oeis.org

8, 64, 168, 760, 2560, 10088, 36456, 138176, 509960, 1910296, 7096320, 26485576, 98590024, 367542080, 1369032168, 5101852856, 19007490560, 70825236904, 263884411560, 983242576576, 3663494987848, 13650146856152, 50859864760320
Offset: 1

Views

Author

R. H. Hardin, Feb 17 2012

Keywords

Comments

Row 4 of A207453.

Examples

			Some solutions for n=5:
  1 0 1 1 1     1 0 1 1 0     0 1 0 1 0     0 1 0 1 1
  1 1 1 1 1     0 1 0 1 0     1 1 1 1 0     0 1 1 1 1
  1 1 1 1 1     0 1 0 1 0     0 1 0 1 0     0 1 0 1 0
  0 1 1 1 1     0 1 0 1 0     0 1 0 1 0     0 1 0 1 0

Links

Crossrefs

Cf. A207453.

Formula

Empirical: a(n) = a(n-1) + 10*a(n-2) + 3*a(n-3) - 9*a(n-4).
Empirical g.f.: 8*x*(1 + 7*x + 3*x^2 - 9*x^3) / (1 - x - 10*x^2 - 3*x^3 + 9*x^4). - Colin Barker, Jun 23 2018

A207456 Number of 5 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.

Original entry on oeis.org

10, 100, 270, 1450, 5200, 23530, 92610, 396100, 1610950, 6754210, 27799200, 115710130, 478341370, 1985702500, 8222193630, 34098329530, 141276194800, 585672013210, 2427100765650, 10060368444100, 41694947333590
Offset: 1

Views

Author

R. H. Hardin, Feb 17 2012

Keywords

Comments

Row 5 of A207453.

Examples

			Some solutions for n=5:
  1 1 1 1 1     1 0 1 1 0     0 1 0 1 0     0 1 0 1 0
  1 1 1 1 1     1 1 0 1 1     1 1 0 1 0     1 1 0 1 0
  0 1 0 1 1     0 1 0 1 0     1 1 0 1 0     0 1 0 1 0
  0 1 0 1 0     0 1 0 1 0     1 1 0 1 0     0 1 0 1 0
  0 1 0 1 0     0 1 0 1 0     1 1 0 1 0     0 1 0 1 0

Links

Crossrefs

Cf. A207453.

Formula

Empirical: a(n) = a(n-1) + 13*a(n-2) + 4*a(n-3) - 16*a(n-4).
Empirical g.f.: 10*x*(1 + 9*x + 4*x^2 - 16*x^3) / (1 - x - 13*x^2 - 4*x^3 + 16*x^4). - Colin Barker, Jun 23 2018

A207457 Number of 6 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.

Original entry on oeis.org

12, 144, 396, 2460, 9216, 46956, 196812, 932688, 4086060, 18819228, 83939328, 382160076, 1717133964, 7780911120, 35067371724, 158593617564, 715647771648, 3233959733292, 14600607874380, 65957362026192, 297845692391532
Offset: 1

Views

Author

R. H. Hardin, Feb 17 2012

Keywords

Comments

Row 6 of A207453.

Examples

			Some solutions for n=5:
  1 0 1 1 0     0 1 1 1 1     1 0 1 0 1     1 0 1 0 1
  1 1 0 1 1     0 1 0 1 1     0 1 1 1 0     1 0 1 0 1
  0 1 0 1 0     0 1 0 1 0     0 1 0 1 0     1 0 1 0 1
  0 1 0 1 0     0 1 0 1 0     0 1 0 1 0     1 0 1 0 0
  0 1 0 1 0     0 1 0 1 0     0 1 0 1 0     1 0 1 0 0
  0 1 0 1 0     0 1 0 1 0     0 1 0 1 0     1 0 1 0 0

Links

Crossrefs

Cf. A207453.

Formula

Empirical: a(n) = a(n-1) + 16*a(n-2) + 5*a(n-3) - 25*a(n-4).
Empirical g.f.: 12*x*(1 + 11*x + 5*x^2 - 25*x^3) / (1 - x - 16*x^2 - 5*x^3 + 25*x^4). - Colin Barker, Jun 23 2018

A207458 Number of 7 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.

Original entry on oeis.org

14, 196, 546, 3850, 14896, 84266, 370734, 1922564, 8935850, 44655394, 212625504, 1045480786, 5031607126, 24563900900, 118782802866, 578049254426, 2801168057744, 13612500276634, 66026807997150, 320661548440324
Offset: 1

Views

Author

R. H. Hardin, Feb 17 2012

Keywords

Comments

Row 7 of A207453.

Examples

			Some solutions for n=5:
  0 1 0 1 0     1 0 1 1 0     1 1 0 1 0     1 1 0 1 1
  0 1 1 1 0     0 1 0 1 0     0 1 0 1 1     1 0 1 0 1
  0 1 0 1 0     0 1 0 1 0     0 1 0 1 1     1 0 1 0 1
  0 1 0 1 0     0 1 0 1 0     0 1 0 1 1     1 0 1 0 0
  0 1 0 1 0     0 1 0 1 0     0 1 0 1 1     1 0 1 0 0
  0 1 0 1 0     0 1 0 1 0     0 1 0 1 1     1 0 1 0 0
  0 1 0 1 0     0 1 0 1 0     0 1 0 1 1     1 0 1 0 0

Links

Crossrefs

Cf. A207453.

Formula

Empirical: a(n) = a(n-1) + 19*a(n-2) + 6*a(n-3) - 36*a(n-4).
Empirical g.f.: 14*x*(1 + 13*x + 6*x^2 - 36*x^3) / ((1 + 2*x - 4*x^2)*(1 - 3*x - 9*x^2)). - Colin Barker, Jun 23 2018
Showing 1-10 of 10 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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