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.

A296948 Number of nX4 0..1 arrays with each 1 adjacent to 1, 3 or 5 king-move neighboring 1s.

Original entry on oeis.org

4, 36, 135, 620, 3637, 17450, 86139, 451210, 2267574, 11420744, 58323254, 295406628, 1495704814, 7596893701, 38524719319, 195316135549, 990921152875, 5025881864695, 25488754160616, 129285719478533, 655737002374833
Offset: 1

Views

Author

R. H. Hardin, Dec 22 2017

Keywords

Comments

Column 4 of A296952.

Examples

			Some solutions for n=7
..0..1..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0. .0..1..1..0
..1..0..0..0. .0..0..0..0. .0..0..1..0. .0..0..0..0. .1..0..1..1
..0..0..1..0. .1..0..0..0. .0..1..0..0. .0..0..0..1. .1..1..1..0
..0..0..1..0. .1..0..0..0. .0..0..0..0. .0..1..0..1. .1..0..0..0
..1..0..1..1. .0..0..0..1. .0..0..1..1. .0..1..0..0. .0..1..1..0
..1..0..1..0. .0..1..1..0. .1..0..1..1. .0..0..0..1. .1..1..1..0
..0..0..1..0. .0..0..0..1. .1..0..1..1. .1..1..0..1. .0..1..0..1

Links

Crossrefs

Cf. A296952.

Formula

Empirical: a(n) = 4*a(n-1) +a(n-2) +68*a(n-3) -196*a(n-4) -26*a(n-5) -1534*a(n-6) +3516*a(n-7) +11*a(n-8) +16575*a(n-9) -30062*a(n-10) +2313*a(n-11) -96450*a(n-12) +131823*a(n-13) -8785*a(n-14) +327240*a(n-15) -317952*a(n-16) -5180*a(n-17) -686278*a(n-18) +424782*a(n-19) +81274*a(n-20) +923710*a(n-21) -239988*a(n-22) -203951*a(n-23) -781908*a(n-24) -144615*a(n-25) +260235*a(n-26) +377172*a(n-27) +354126*a(n-28) -188055*a(n-29) -54273*a(n-30) -267279*a(n-31) +89538*a(n-32) -40496*a(n-33) +109321*a(n-34) -28907*a(n-35) +24197*a(n-36) -26006*a(n-37) +6172*a(n-38) -5803*a(n-39) +3713*a(n-40) -928*a(n-41) +751*a(n-42) -331*a(n-43) +76*a(n-44) -42*a(n-45) +12*a(n-46)

A296946 Number of n X 2 0..1 arrays with each 1 adjacent to 1, 3 or 5 king-move neighboring 1s.

Original entry on oeis.org

2, 8, 16, 36, 112, 256, 608, 1680, 4064, 9920, 25984, 64320, 159232, 407296, 1017344, 2536704, 6420992, 16093184, 40271872, 101471232, 254636032, 638328832, 1605165056, 4029763584, 10110525440, 25402425344, 63780978688, 160088997888
Offset: 1

Views

Author

R. H. Hardin, Dec 22 2017

Keywords

Examples

			Some solutions for n=7:
..0..0. .1..1. .1..1. .1..0. .1..1. .1..1. .0..1. .1..1. .0..0. .0..0
..1..1. .0..0. .0..0. .0..1. .0..0. .0..0. .0..1. .1..1. .0..0. .1..1
..0..0. .1..1. .0..1. .1..1. .0..1. .1..1. .1..1. .1..1. .0..0. .1..1
..1..1. .0..0. .0..1. .1..0. .0..1. .1..1. .1..0. .0..0. .1..1. .0..0
..0..0. .0..0. .0..0. .1..0. .1..1. .0..0. .0..1. .1..1. .1..1. .1..1
..0..0. .0..1. .0..1. .0..0. .0..1. .0..1. .0..0. .0..0. .0..0. .1..1
..1..1. .0..1. .1..0. .1..1. .1..0. .1..0. .0..0. .0..0. .1..1. .1..1

Links

Crossrefs

Column 2 of A296952.

Formula

Empirical: a(n) = 2*a(n-1) + 8*a(n-3) - 12*a(n-4).
Empirical g.f.: 2*x*(1 + 2*x - 6*x^3) / (1 - 2*x - 8*x^3 + 12*x^4). - Colin Barker, Feb 25 2019

A296947 Number of n X 3 0..1 arrays with each 1 adjacent to 1, 3 or 5 king-move neighboring 1s.

Original entry on oeis.org

3, 16, 45, 135, 544, 1765, 5763, 20811, 70207, 236330, 822902, 2806042, 9547539, 32855983, 112351535, 383730987, 1315580367, 4501742568, 15396061261, 52720880494, 180431027632, 617365998304, 2113260768118, 7232567686580
Offset: 1

Views

Author

R. H. Hardin, Dec 22 2017

Keywords

Comments

Column 3 of A296952.

Examples

			Some solutions for n=7:
..0..0..0. .1..0..0. .1..1..1. .0..0..0. .0..1..1. .0..0..0. .0..0..0
..1..1..0. .1..0..1. .1..1..1. .0..0..1. .0..1..1. .1..0..1. .1..1..1
..0..0..0. .0..0..1. .0..0..0. .1..0..1. .0..0..0. .0..1..0. .1..1..1
..0..0..1. .0..1..1. .1..1..0. .1..0..0. .0..1..1. .0..0..1. .0..0..0
..0..0..1. .0..0..1. .0..0..0. .0..0..0. .0..1..1. .0..0..0. .0..0..0
..1..0..0. .1..1..0. .1..0..1. .1..1..0. .0..1..1. .1..0..0. .1..0..0
..0..1..0. .0..0..1. .1..0..1. .0..0..0. .0..0..0. .0..1..0. .1..0..0

Links

Crossrefs

Cf. A296952.

Formula

Empirical: a(n) = 3*a(n-1) +a(n-2) +16*a(n-3) -46*a(n-4) -20*a(n-5) -19*a(n-6) +148*a(n-7) +64*a(n-8) -58*a(n-9) -180*a(n-10) +9*a(n-11) +70*a(n-12) +35*a(n-13) -29*a(n-14) -13*a(n-15) +7*a(n-16) +6*a(n-17) +a(n-18) -2*a(n-19).

A296949 Number of nX5 0..1 arrays with each 1 adjacent to 1, 3 or 5 king-move neighboring 1s.

Original entry on oeis.org

6, 112, 544, 3637, 37179, 256713, 1898178, 16087936, 121741279, 933686077, 7473862911, 57912910897, 449682762989, 3538407928642, 27585262869841, 215073549972468, 1683740352779281, 13146690679835447, 102637633797615262
Offset: 1

Views

Author

R. H. Hardin, Dec 22 2017

Keywords

Comments

Column 5 of A296952.

Examples

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

Links

Crossrefs

Cf. A296952.

A296950 Number of nX6 0..1 arrays with each 1 adjacent to 1, 3 or 5 king-move neighboring 1s.

Original entry on oeis.org

9, 256, 1765, 17450, 256713, 2640993, 29067775, 356242817, 4007327435, 45579824373, 533089787086, 6110543663491, 70142323962609, 810920084478849, 9331277910756214, 107381182592973180, 1237942191372084761
Offset: 1

Views

Author

R. H. Hardin, Dec 22 2017

Keywords

Comments

Column 6 of A296952.

Examples

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

Links

Crossrefs

Cf. A296952.

A296951 Number of nX7 0..1 arrays with each 1 adjacent to 1, 3 or 5 king-move neighboring 1s.

Original entry on oeis.org

13, 608, 5763, 86139, 1898178, 29067775, 482228052, 8786244680, 148081034460, 2527093956658, 44081436520906, 756410616073885, 13001520369777372, 224610561730578221, 3867018822679814785, 66587006212100036798
Offset: 1

Views

Author

R. H. Hardin, Dec 22 2017

Keywords

Comments

Column 7 of A296952.

Examples

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

Links

Crossrefs

Cf. A296952.

A296945 Number of n X n 0..1 arrays with each 1 adjacent to 1, 3 or 5 king-move neighboring 1's.

Original entry on oeis.org

1, 8, 45, 620, 37179, 2640993, 482228052, 246430289779, 233010334725043, 513658708035556281
Offset: 1

Views

Author

R. H. Hardin, Dec 22 2017

Keywords

Comments

Diagonal of A296952.

Examples

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

Crossrefs

Cf. A296952.
Showing 1-7 of 7 results.

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