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 1-9 of 9 results.

A208282 Number of n X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically.

Original entry on oeis.org

2, 16, 102, 984, 9900, 119580, 1604862, 24229696, 403795242, 7388858420, 147219127000, 3175214941800, 73720244775658, 1833809960513104, 48667824127404150, 1372862920890984032, 41025768742532649684
Offset: 1

Views

Author

R. H. Hardin Feb 25 2012

Keywords

Comments

Diagonal of A208287

Examples

			Some solutions for n=4
..1..1..1..1....1..1..0..0....1..0..1..0....0..1..1..0....1..1..1..0
..0..1..0..1....1..0..1..0....1..1..0..1....0..1..1..0....0..1..1..0
..1..1..1..1....1..1..0..0....1..1..1..1....0..1..1..0....1..1..1..0
..0..1..0..1....1..1..1..0....1..1..1..1....0..1..1..0....1..1..1..0

Links

A208283 Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically.

Original entry on oeis.org

10, 100, 378, 984, 2090, 3900, 6650, 10608, 16074, 23380, 32890, 45000, 60138, 78764, 101370, 128480, 160650, 198468, 242554, 293560, 352170, 419100, 495098, 580944, 677450, 785460, 905850, 1039528, 1187434, 1350540, 1529850, 1726400, 1941258
Offset: 1

Views

Author

R. H. Hardin, Feb 25 2012

Keywords

Comments

Column 4 of A208287.

Examples

			Some solutions for n=4:
..1..1..1..0....0..1..0..0....1..0..1..1....1..1..1..1....1..1..1..1
..1..1..0..0....0..1..0..1....0..1..1..1....0..1..0..1....1..1..1..1
..1..1..1..0....0..1..0..1....0..1..1..1....1..1..1..1....1..1..1..1
..1..1..1..0....0..1..0..1....0..1..1..1....0..1..0..1....1..1..1..1

Links

Crossrefs

Cf. A208287.

Formula

Empirical: a(n) = (4/3)*n^4 + 10*n^3 + (2/3)*n^2 - 2*n.
Conjectures from Colin Barker, Jun 29 2018: (Start)
G.f.: 2*x*(5 + 25*x - 11*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)

A208284 Number of n X 5 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically.

Original entry on oeis.org

16, 256, 1260, 3984, 9900, 21096, 40376, 71360, 118584, 187600, 285076, 418896, 598260, 833784, 1137600, 1523456, 2006816, 2604960, 3337084, 4224400, 5290236, 6560136, 8061960, 9825984, 11885000, 14274416, 17032356, 20199760, 23820484
Offset: 1

Views

Author

R. H. Hardin, Feb 25 2012

Keywords

Comments

Column 5 of A208287.

Examples

			Some solutions for n=4:
..0..1..0..1..0....0..1..0..1..0....0..1..0..1..1....1..0..1..1..1
..1..0..1..0..0....1..1..0..1..1....0..1..0..1..0....0..1..0..1..1
..1..1..0..1..0....1..1..0..1..0....0..1..0..1..0....0..1..1..1..1
..1..1..0..1..0....1..1..0..1..0....0..1..0..1..0....0..1..1..1..1

Links

Crossrefs

Cf. A208287.

Formula

Empirical: a(n) = (5/6)*n^5 + 9*n^4 + (91/6)*n^3 - 9*n^2.
Conjectures from Colin Barker, Jun 29 2018: (Start)
G.f.: 4*x*(2 - x)*(2 + 21*x + 6*x^2 - 4*x^3) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
(End)

A208285 Number of n X 6 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically.

Original entry on oeis.org

26, 676, 4374, 16872, 49130, 119580, 256774, 502416, 914778, 1572500, 2578774, 4065912, 6200298, 9187724, 13279110, 18776608, 26040090, 35494020, 47634710, 63037960, 82367082, 106381308, 135944582, 172034736, 215753050, 268334196
Offset: 1

Views

Author

R. H. Hardin, Feb 25 2012

Keywords

Comments

Column 6 of A208287.

Examples

			Some solutions for n=4:
..0..1..0..1..1..0....0..1..1..1..1..0....1..1..1..1..0..0....1..0..1..0..1..0
..0..1..0..1..0..1....1..0..1..1..0..1....1..1..0..1..1..1....0..1..0..1..0..1
..0..1..0..1..0..0....0..1..1..1..1..0....1..1..1..1..0..0....1..0..1..0..1..0
..0..1..0..1..0..0....1..1..1..1..0..1....1..1..0..1..1..0....1..0..1..1..1..1

Links

Crossrefs

Cf. A208287.

Formula

Empirical: a(n) = (8/15)*n^6 + (23/3)*n^5 + (82/3)*n^4 + (1/3)*n^3 - (178/15)*n^2 + 2*n.
Conjectures from Colin Barker, Jun 29 2018: (Start)
G.f.: 2*x*(13 + 247*x + 94*x^2 - 230*x^3 + 65*x^4 + 3*x^5) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)

A208286 Number of n X 7 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically.

Original entry on oeis.org

42, 1764, 14946, 70216, 239490, 665892, 1604862, 3478160, 6942474, 12974340, 22973082, 38883480, 63339874, 99833412, 152904150, 228359712, 333522218, 477505188, 671522130, 929228520, 1267098882, 1704840676, 2265846702
Offset: 1

Views

Author

R. H. Hardin, Feb 25 2012

Keywords

Comments

Column 7 of A208287.

Examples

			Some solutions for n=4:
..1..1..0..1..1..1..0....1..0..1..1..0..1..1....1..0..1..1..1..0..0
..1..1..1..0..1..1..0....0..1..0..1..1..1..1....0..1..0..1..1..0..1
..1..1..1..1..1..1..0....1..0..1..1..0..1..1....0..1..1..1..1..0..1
..1..1..1..0..1..1..0....1..0..1..1..1..1..1....0..1..1..1..1..0..1

Links

Crossrefs

Cf. A208287.

Formula

Empirical: a(n) = (61/180)*n^7 + (121/20)*n^6 + (1157/36)*n^5 + (425/12)*n^4 - (2923/90)*n^3 - (22/15)*n^2 + 2*n.
Conjectures from Colin Barker, Jun 29 2018: (Start)
G.f.: 2*x*(21 + 714*x + 1005*x^2 - 1156*x^3 + 203*x^4 + 86*x^5 - 19*x^6) / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
(End)

A208288 Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically.

Original entry on oeis.org

8, 64, 216, 984, 3984, 16872, 70216, 294192, 1229400, 5142728, 21504256, 89933368, 376090120, 1572797488, 6577333928, 27506063752, 115028758000, 481043815944, 2011697870456, 8412806681456, 35181880551080, 147128631386264
Offset: 1

Views

Author

R. H. Hardin, Feb 25 2012

Keywords

Comments

Row 4 of A208287.

Examples

			Some solutions for n=4:
..0..1..1..0....1..1..0..0....1..0..1..0....0..1..1..0....1..0..1..1
..1..1..0..0....1..0..1..0....0..1..0..0....0..1..1..0....0..1..1..0
..1..1..0..0....1..1..0..0....1..1..1..0....0..1..1..0....1..0..1..1
..1..1..0..0....1..1..1..0....0..1..1..0....0..1..1..0....0..1..1..1

Links

Crossrefs

Cf. A208287.

Formula

Empirical: a(n) = 3*a(n-1) + 6*a(n-2) - 4*a(n-3) - 2*a(n-4) + a(n-5).
Empirical g.f.: 8*x*(1 + 5*x - 3*x^2 - 2*x^3 + x^4) / ((1 + x - x^2)*(1 - 4*x - x^2 + x^3)). - Colin Barker, Jun 30 2018

A208289 Number of 5 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically.

Original entry on oeis.org

10, 100, 390, 2090, 9900, 49130, 239490, 1175440, 5754050, 28195750, 138110340, 676601470, 3314477450, 16237031560, 79541647910, 389658289890, 1908854053840, 9351079145150, 45808984336150, 224408665354600, 1099331244406030
Offset: 1

Views

Author

R. H. Hardin, Feb 25 2012

Keywords

Comments

Row 5 of A208287.

Examples

			Some solutions for n=4:
..0..1..0..0....1..0..1..0....0..1..0..1....0..1..0..0....1..1..1..1
..1..1..1..0....0..1..1..0....1..0..1..1....1..1..1..1....1..1..1..1
..1..1..0..0....1..1..1..0....1..0..1..1....0..1..1..1....1..1..1..1
..1..1..1..0....1..1..1..0....1..0..1..1....1..1..1..1....1..1..1..1
..1..1..1..0....1..1..1..0....1..0..1..1....1..1..1..1....1..1..1..1

Links

Crossrefs

Cf. A208287.

Formula

Empirical: a(n) = 3*a(n-1) + 10*a(n-2) - 2*a(n-3) - 7*a(n-4) + a(n-6).
Empirical g.f.: 10*x*(1 + 7*x - x^2 - 6*x^3 + x^5) / (1 - 3*x - 10*x^2 + 2*x^3 + 7*x^4 - x^6). - Colin Barker, Jun 30 2018

A208290 Number of 6 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically.

Original entry on oeis.org

12, 144, 636, 3900, 21096, 119580, 665892, 3733080, 20874900, 116842500, 653759952, 3658440924, 20471559852, 114555114720, 641024680212, 3587040344820, 20072307438840, 112320368080068, 628520819264292
Offset: 1

Views

Author

R. H. Hardin, Feb 25 2012

Keywords

Comments

Row 6 of A208287.

Examples

			Some solutions for n=4:
..0..1..1..0....0..1..1..0....1..1..0..1....0..1..0..0....1..1..1..1
..0..1..0..1....0..1..1..0....1..1..0..0....1..0..1..1....0..1..1..1
..0..1..0..1....0..1..1..0....1..1..0..0....1..1..1..1....1..1..1..1
..0..1..0..1....0..1..1..0....1..1..0..0....1..0..1..1....1..1..1..1
..0..1..0..1....0..1..1..0....1..1..0..0....1..1..1..1....1..1..1..1
..0..1..0..1....0..1..1..0....1..1..0..0....1..0..1..1....1..1..1..1

Links

Crossrefs

Cf. A208287.

Formula

Empirical: a(n) = 4*a(n-1) + 11*a(n-2) - 10*a(n-3) - 10*a(n-4) + 6*a(n-5) + 2*a(n-6) - a(n-7).
Empirical g.f.: 12*x*(1 - x)*(1 + 9*x + 3*x^2 - 6*x^3 - x^4 + x^5) / (1 - 4*x - 11*x^2 + 10*x^3 + 10*x^4 - 6*x^5 - 2*x^6 + x^7). - Colin Barker, Jun 30 2018

A208291 Number of 7 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically.

Original entry on oeis.org

14, 196, 966, 6650, 40376, 256774, 1604862, 10095932, 63357434, 397965218, 2498872432, 15692738782, 98544531778, 618833962068, 3886089661790, 24403526661710, 153246991242128, 962346508543154, 6043255215031230
Offset: 1

Views

Author

R. H. Hardin, Feb 25 2012

Keywords

Comments

Row 7 of A208287.

Examples

			Some solutions for n=4:
..0..1..0..1....0..1..1..1....1..0..1..1....0..1..1..1....1..0..1..0
..1..0..1..0....1..1..0..0....1..0..1..0....1..0..1..1....1..0..1..0
..0..1..0..0....1..1..0..1....1..0..1..0....1..0..1..1....1..0..1..0
..1..1..0..0....1..1..0..0....1..0..1..0....1..0..1..1....1..0..1..0
..0..1..0..0....1..1..0..1....1..0..1..0....1..0..1..1....1..0..1..0
..1..1..0..0....1..1..0..0....1..0..1..0....1..0..1..1....1..0..1..0
..0..1..0..0....1..1..0..0....1..0..1..0....1..0..1..1....1..0..1..0

Links

Crossrefs

Cf. A208287.

Formula

Empirical: a(n) = 4*a(n-1) + 16*a(n-2) - 7*a(n-3) - 23*a(n-4) + 2*a(n-5) + 9*a(n-6) - a(n-8).
Empirical g.f.: 14*x*(1 + x)*(1 + 9*x - 12*x^2 - 6*x^3 + 7*x^4 + x^5 - x^6) / (1 - 4*x - 16*x^2 + 7*x^3 + 23*x^4 - 2*x^5 - 9*x^6 + x^8). - Colin Barker, Jun 30 2018
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