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 1-7 of 7 results.

A183444 Number of n X 3 binary arrays with every 1 having exactly two king-move neighbors equal to 1.

Original entry on oeis.org

1, 9, 18, 30, 107, 265, 553, 1505, 3852, 8922, 22477, 56889, 137617, 340401, 851098, 2091618, 5160851, 12817517, 31655009, 78159377, 193558964, 478614470, 1182673261, 2925763109, 7235864705, 17887850273, 44237338898, 109401520982
Offset: 1

Views

Author

R. H. Hardin, Jan 04 2011

Keywords

Comments

Column 3 of A183450.

Examples

			Some solutions for 5 X 3:
..0..1..0....1..1..0....0..0..0....0..0..0....1..1..0....0..0..0....0..0..1
..0..1..1....1..0..0....0..1..1....0..1..0....0..1..0....0..0..0....0..1..1
..0..0..0....0..0..0....0..0..1....1..0..1....0..0..0....0..0..0....0..0..0
..0..1..0....0..1..1....1..0..0....1..0..1....1..0..0....1..1..0....1..0..0
..1..1..0....0..0..1....1..1..0....0..1..0....1..1..0....1..0..0....1..1..0
		

Crossrefs

Cf. A183450.

Formula

Empirical: a(n) = 2*a(n-1) - a(n-2) + 8*a(n-3) - 7*a(n-4) + 2*a(n-5) - 2*a(n-6).
Empirical g.f.: x*(1 + 7*x + x^2 - 5*x^3 - 2*x^5) / (1 - 2*x + x^2 - 8*x^3 + 7*x^4 - 2*x^5 + 2*x^6). - Colin Barker, Feb 27 2018

A183445 Number of n X 4 binary arrays with every 1 having exactly two king-move neighbors equal to 1.

Original entry on oeis.org

1, 13, 30, 72, 283, 831, 2399, 7761, 23840, 72396, 225569, 696929, 2144537, 6635889, 20510002, 63318408, 195704391, 604826763, 1868678179, 5774848073, 17846507936, 55148861000, 170427655945, 526681961257, 1627610746225, 5029867948101
Offset: 1

Views

Author

R. H. Hardin, Jan 04 2011

Keywords

Comments

Column 4 of A183450.

Examples

			Some solutions for 5 X 4:
..0..1..0..0....1..1..0..0....0..1..1..0....0..1..0..0....0..0..1..0
..1..0..1..0....0..1..0..0....0..0..1..0....1..1..0..0....0..1..1..0
..1..0..1..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..1..0..0....1..1..0..0....0..1..0..0....0..1..0..0....1..0..0..0
..0..0..0..0....0..1..0..0....1..1..0..0....0..1..1..0....1..1..0..0
		

Crossrefs

Cf. A183450.

Formula

Empirical: a(n) = 3*a(n-1) + a(n-2) + 5*a(n-3) - 18*a(n-4) - 16*a(n-5) + 7*a(n-6) + 3*a(n-7) + a(n-8) - a(n-9).
Empirical g.f.: x*(1 + x)*(1 + 9*x - 19*x^2 - 17*x^3 + 7*x^4 + 3*x^5 + x^6 - x^7) / (1 - 3*x - x^2 - 5*x^3 + 18*x^4 + 16*x^5 - 7*x^6 - 3*x^7 - x^8 + x^9). - Colin Barker, Mar 29 2018

A183446 Number of nX5 binary arrays with every 1 having exactly two king-move neighbors equal to 1.

Original entry on oeis.org

1, 33, 107, 283, 2054, 9208, 34867, 176949, 833001, 3619285, 16979210, 79536106, 362125386, 1678147584, 7816357207, 36107427015, 167380756056, 778109691292, 3610178963149, 16759752441151, 77893373268254, 361906632299828
Offset: 1

Views

Author

R. H. Hardin Jan 04 2011

Keywords

Comments

Column 5 of A183450

Examples

			Some solutions for 7X5
..0..1..1..0..0....0..0..0..0..0....0..0..0..1..1....0..0..0..0..0
..1..0..0..1..0....0..1..0..0..0....1..1..0..1..0....0..0..0..0..0
..0..1..1..0..0....1..1..0..1..0....1..0..0..0..0....0..1..0..0..0
..0..0..0..0..0....0..0..0..1..1....0..0..0..0..0....1..1..0..0..0
..1..0..0..0..0....1..1..0..0..0....0..0..0..0..0....0..0..0..0..0
..1..1..0..1..1....0..1..0..0..1....1..0..0..1..0....0..1..0..0..0
..0..0..0..1..0....0..0..0..1..1....1..1..0..1..1....0..1..1..0..0
		

Formula

Empirical: a(n)=6*a(n-1)-4*a(n-2)+26*a(n-3)-181*a(n-4)-17*a(n-5)+101*a(n-6)+1148*a(n-7)-826*a(n-8)+575*a(n-9)-429*a(n-10)-160*a(n-11)-83*a(n-12)-913*a(n-13)-799*a(n-14)+405*a(n-15)+185*a(n-16)+74*a(n-17)-8*a(n-18)-33*a(n-19)+6*a(n-20)

A183447 Number of nX6 binary arrays with every 1 having exactly two king-move neighbors equal to 1.

Original entry on oeis.org

1, 69, 265, 831, 9208, 53608, 257733, 1817225, 11414889, 65073225, 412023374, 2584580914, 15632039022, 96988632570, 604295047829, 3722359557561, 23052411911880, 143185736751014, 886632358849607, 5495153241025073
Offset: 1

Views

Author

R. H. Hardin Jan 04 2011

Keywords

Comments

Column 6 of A183450

Examples

			Some solutions for 5X6
..1..0..0..1..1..0....0..0..0..0..1..0....0..1..0..1..1..0....1..1..0..1..0..0
..1..1..0..0..1..0....0..0..1..1..0..1....1..1..0..0..1..0....1..0..0..1..1..0
..0..0..0..0..0..0....0..1..0..0..0..1....0..0..0..0..0..0....0..0..0..0..0..0
..1..0..0..0..1..0....1..0..0..1..0..1....0..0..1..0..1..0....1..1..0..0..0..1
..1..1..0..0..1..1....0..1..1..0..1..0....0..1..1..0..1..1....1..0..0..0..1..1
		

Formula

Empirical: a(n)=8*a(n-1)-7*a(n-2)+68*a(n-3)-653*a(n-4)+32*a(n-5)+485*a(n-6)+14641*a(n-7)-6637*a(n-8)-8411*a(n-9)-106883*a(n-10)-56160*a(n-11)+237056*a(n-12)+223756*a(n-13)+325584*a(n-14)-437989*a(n-15)-356189*a(n-16)-703364*a(n-17)-310700*a(n-18)-8533*a(n-19)+149004*a(n-20)+97683*a(n-21)-213560*a(n-22)-308877*a(n-23)-121132*a(n-24)-130124*a(n-25)-91121*a(n-26)+125661*a(n-27)-25407*a(n-28)-35027*a(n-29)-22817*a(n-30)+17965*a(n-31)-44181*a(n-32)+3667*a(n-33)-1494*a(n-34)-2839*a(n-35)+619*a(n-36)-540*a(n-37)+209*a(n-38)-67*a(n-39)+35*a(n-40)-4*a(n-41)

A183448 Number of nX7 binary arrays with every 1 having exactly two king-move neighbors equal to 1.

Original entry on oeis.org

1, 121, 553, 2399, 34867, 257733, 1744887, 16192521, 132651622, 1038281076, 8774615462, 72803921204, 594525068675, 4940133605905, 40989589283304, 338552166728150, 2806660250827517, 23275769947149983, 192804453727767520
Offset: 1

Views

Author

R. H. Hardin Jan 04 2011

Keywords

Comments

Column 7 of A183450

Examples

			Some solutions for 5X7
..0..1..1..0..0..0..0....0..0..0..0..1..0..0....0..1..1..0..1..0..0
..1..0..0..1..0..0..0....0..0..0..1..1..0..0....0..0..1..0..1..1..0
..1..0..1..0..0..0..0....0..0..0..0..0..0..0....1..0..0..0..0..0..0
..0..1..0..0..1..0..0....0..0..0..0..0..1..1....1..1..0..0..1..1..0
..0..0..0..1..1..0..0....0..0..0..0..0..1..0....0..0..0..0..0..1..0
		

A183449 Number of nX8 binary arrays with every 1 having exactly two king-move neighbors equal to 1.

Original entry on oeis.org

1, 253, 1505, 7761, 176949, 1817225, 16192521, 216103851, 2491241396, 26807184942, 319246780548, 3727927654904, 42498891259325, 496063346878031, 5787799084661820, 67059980281582582, 780988033705277709
Offset: 1

Views

Author

R. H. Hardin Jan 04 2011

Keywords

Comments

Column 8 of A183450

Examples

			Some solutions for 5X8
..0..1..0..0..1..1..0..0....0..1..0..0..0..0..0..0....0..0..0..0..0..0..0..0
..1..1..0..0..1..0..0..1....0..1..1..0..0..1..1..0....0..0..1..0..0..0..1..1
..0..0..0..0..0..0..1..1....0..0..0..0..1..0..0..1....0..1..1..0..0..0..1..0
..1..0..0..0..0..0..0..0....1..1..0..0..0..1..1..0....0..0..0..0..1..0..0..0
..1..1..0..0..0..0..0..0....1..0..0..0..0..0..0..0....0..0..0..0..1..1..0..0
		

A183443 Number of n X n binary arrays with every 1 having exactly two king-move neighbors equal to 1.

Original entry on oeis.org

1, 5, 18, 72, 2054, 53608, 1744887, 216103851, 39184763856, 11314547102638, 7873316318240100, 9711485486581483616, 21262647899259681841579
Offset: 1

Views

Author

R. H. Hardin Jan 04 2011

Keywords

Comments

Diagonal of A183450

Examples

			Some solutions for 5X5
..0..0..0..0..0....0..0..0..1..0....0..0..1..0..0....0..1..0..0..0
..1..0..0..0..0....0..1..1..0..1....0..1..0..1..0....1..1..0..1..0
..1..1..0..1..1....1..0..0..0..1....1..0..0..0..1....0..0..0..1..1
..0..0..0..0..1....1..0..0..0..1....1..0..0..0..1....1..1..0..0..0
..0..0..0..0..0....0..1..1..1..0....0..1..1..1..0....0..1..0..0..0
		
Showing 1-7 of 7 results.