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.

A282785 Number of n X 2 0..1 arrays with no 1 equal to more than one of its king-move neighbors, with the exception of exactly one element.

Original entry on oeis.org

0, 0, 8, 16, 72, 240, 736, 2352, 7128, 21424, 63768, 187424, 547136, 1586016, 4570280, 13105488, 37414632, 106404944, 301580704, 852159120, 2401326712, 6750087408, 18931901880, 52989773184, 148039566336, 412873929408, 1149659579720
Offset: 1

Views

Author

R. H. Hardin, Feb 21 2017

Keywords

Examples

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

Links

Crossrefs

Column 2 of A282791.

Formula

Empirical: a(n) = 2*a(n-1) + 5*a(n-2) +2*a(n-3) - 17*a(n-4) - 24*a(n-5) - 16*a(n-6).
Empirical g.f.: 8*x^3 / (1 - x - 3*x^2 - 4*x^3)^2. - Colin Barker, Feb 21 2019

A282786 Number of nX3 0..1 arrays with no 1 equal to more than one of its king-move neighbors, with the exception of exactly one element.

Original entry on oeis.org

1, 8, 73, 318, 1747, 8216, 38027, 173722, 773529, 3412416, 14880845, 64319686, 276057515, 1177345064, 4994757435, 21091941082, 88706514017, 371741444080, 1552891025645, 6468454612966, 26874623008899, 111396556833528
Offset: 1

Views

Author

R. H. Hardin, Feb 21 2017

Keywords

Comments

Column 3 of A282791.

Examples

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

Links

Crossrefs

Cf. A282791.

Formula

Empirical: a(n) = 4*a(n-1) +8*a(n-2) -8*a(n-3) -78*a(n-4) -72*a(n-5) -16*a(n-6) +64*a(n-7) -33*a(n-8) +52*a(n-9) -24*a(n-10) +8*a(n-11) -4*a(n-12)

A282787 Number of n X 4 0..1 arrays with no 1 equal to more than one of its king-move neighbors, with the exception of exactly one element.

Original entry on oeis.org

2, 16, 318, 1952, 16584, 119176, 832218, 5780340, 39020884, 260919192, 1725189008, 11301829056, 73518360532, 475188725292, 3055000301306, 19549420762100, 124588203699132, 791140457595836, 5007656160113482, 31605725372441888
Offset: 1

Views

Author

R. H. Hardin, Feb 21 2017

Keywords

Comments

Column 4 of A282791.

Examples

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

Links

Crossrefs

Cf. A282791.

Formula

Empirical: a(n) = 4*a(n-1) +28*a(n-2) +26*a(n-3) -404*a(n-4) -1508*a(n-5) -2631*a(n-6) -1242*a(n-7) +1650*a(n-8) +5880*a(n-9) +5486*a(n-10) +2762*a(n-11) -2635*a(n-12) -3886*a(n-13) -3543*a(n-14) -896*a(n-15) -39*a(n-16) +322*a(n-17) -49*a(n-18).

A282788 Number of nX5 0..1 arrays with no 1 equal to more than one of its king-move neighbors, with the exception of exactly one element.

Original entry on oeis.org

5, 72, 1747, 16584, 208559, 2207352, 22998587, 236744562, 2372235577, 23556868268, 231170201002, 2248366154372, 21712536566614, 208339762352392, 1988486114090520, 18890627682669588, 178728457004534603
Offset: 1

Views

Author

R. H. Hardin, Feb 21 2017

Keywords

Comments

Column 5 of A282791.

Examples

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

Links

Crossrefs

Cf. A282791.

Formula

Empirical: a(n) = 8*a(n-1) +46*a(n-2) +6*a(n-3) -2183*a(n-4) -7382*a(n-5) -11643*a(n-6) +54132*a(n-7) +102965*a(n-8) +292502*a(n-9) -793634*a(n-10) +465944*a(n-11) -5549560*a(n-12) +11071058*a(n-13) -20451847*a(n-14) +66051624*a(n-15) -119880393*a(n-16) +200181288*a(n-17) -351381924*a(n-18) +424696584*a(n-19) -467540195*a(n-20) +542912638*a(n-21) -445397634*a(n-22) +369091666*a(n-23) -353980998*a(n-24) +201536626*a(n-25) -145556750*a(n-26) +127195728*a(n-27) -40377766*a(n-28) +34252470*a(n-29) -28331987*a(n-30) +3136852*a(n-31) -5045600*a(n-32) +3837652*a(n-33) -360550*a(n-34) +205482*a(n-35) -439128*a(n-36) +4656*a(n-37) -5817*a(n-38) +21150*a(n-39) -3141*a(n-40) -1260*a(n-41) -900*a(n-42)

A282789 Number of nX6 0..1 arrays with no 1 equal to more than one of its king-move neighbors, with the exception of exactly one element.

Original entry on oeis.org

12, 240, 8216, 119176, 2207352, 34974844, 545174028, 8385651160, 125782952202, 1869100531456, 27455017613694, 399770700356992, 5779997586129870, 83043999837342288, 1186866407744919094, 16884581390750904832
Offset: 1

Views

Author

R. H. Hardin, Feb 21 2017

Keywords

Comments

Column 6 of A282791.

Examples

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

Links

Crossrefs

Cf. A282791.

Formula

Empirical recurrence of order 60 (see link above)

A282790 Number of nX7 0..1 arrays with no 1 equal to more than one of its king-move neighbors, with the exception of exactly one element.

Original entry on oeis.org

26, 736, 38027, 832218, 22998587, 545174028, 12713143876, 292288389872, 6555156469894, 145619095090322, 3197415688277735, 69595512931794512, 1504085477252415247, 32301337050939080872, 690041423059410095352
Offset: 1

Views

Author

R. H. Hardin, Feb 21 2017

Keywords

Comments

Column 7 of A282791.

Examples

			Some solutions for n=3
..1..0..1..1..0..1..0. .0..0..0..1..0..0..0. .1..0..0..0..1..0..0
..0..0..0..0..0..0..1. .1..0..0..0..1..0..0. .0..0..0..1..0..0..0
..0..0..1..0..0..0..1. .1..0..1..0..1..0..0. .0..1..0..0..1..0..1

Links

Crossrefs

Cf. A282791.

A282784 Number of n X n 0..1 arrays with no 1 equal to more than one of its king-move neighbors, with the exception of exactly one element.

Original entry on oeis.org

0, 0, 73, 1952, 208559, 34974844, 12713143876, 10031326473244, 16844842566734425, 61957626701788646084, 497581272671041376917187
Offset: 1

Views

Author

R. H. Hardin, Feb 21 2017

Keywords

Comments

Diagonal of A282791.

Examples

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

Crossrefs

Cf. A282791.
Showing 1-7 of 7 results.

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

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