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 1-6 of 6 results.

A303713 Number of n X n 0..1 arrays with every element unequal to 0, 1 or 5 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 1, 5, 17, 81, 343, 1592, 7551, 34546, 158402, 734321, 3389249, 15610239, 72045856, 332515175, 1533661362, 7075164898, 32644176977, 150600651761, 694773927239, 3205360278072, 14787893322847, 68223139662242, 314745564736962
Offset: 1

Views

Author

R. H. Hardin, Apr 29 2018

Keywords

Comments

Diagonal of A303719.

Examples

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

Links

Crossrefs

Cf. A303719.

Formula

Empirical: a(n) = 3*a(n-1) +2*a(n-2) +28*a(n-3) -2*a(n-4) -42*a(n-5) -56*a(n-6) +50*a(n-7) -44*a(n-8) +30*a(n-9) -44*a(n-10) +2*a(n-11) +2*a(n-12) -a(n-14) +a(n-15) for n>18.

A303714 Number of n X 3 0..1 arrays with every element unequal to 0, 1 or 5 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

3, 3, 5, 8, 14, 24, 40, 68, 116, 196, 332, 564, 956, 1620, 2748, 4660, 7900, 13396, 22716, 38516, 65308, 110740, 187772, 318388, 539868, 915412, 1552188, 2631924, 4462748, 7567124, 12830972, 21756468, 36890716, 62552660, 106065596, 179847028
Offset: 1

Views

Author

R. H. Hardin, Apr 29 2018

Keywords

Comments

Column 3 of A303719.

Examples

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

Links

Crossrefs

Cf. A303719.

Formula

Empirical: a(n) = a(n-1) +2*a(n-3) for n>4.
Empirical g.f.: 3*x-x^2*(3+2*x+3*x^2)/(-1+x+2*x^3). - R. J. Mathar, Apr 30 2018

A303715 Number of nX4 0..1 arrays with every element unequal to 0, 1 or 5 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

5, 5, 8, 17, 36, 76, 161, 349, 749, 1604, 3449, 7412, 15912, 34177, 73421, 157693, 338696, 727505, 1562612, 3356300, 7209009, 15484261, 33258581, 71436052, 153437513, 329568260, 707879240, 1520453249, 3265780149, 7014565813
Offset: 1

Views

Author

R. H. Hardin, Apr 29 2018

Keywords

Comments

Column 4 of A303719.

Examples

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

Links

Crossrefs

Cf. A303719.

Formula

Empirical: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6)

A303716 Number of nX5 0..1 arrays with every element unequal to 0, 1 or 5 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

8, 7, 14, 36, 81, 169, 361, 784, 1681, 3600, 7744, 16641, 35721, 76729, 164836, 354025, 760384, 1633284, 3508129, 7535025, 16184529, 34762816, 74666881, 160376896, 344473600, 739894401, 1589218225, 3413480625, 7331811876, 15747991081
Offset: 1

Views

Author

R. H. Hardin, Apr 29 2018

Keywords

Comments

Column 5 of A303719.

Examples

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

Links

Crossrefs

Cf. A303719.

Formula

Empirical: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6) for n>9

A303717 Number of nX6 0..1 arrays with every element unequal to 0, 1 or 5 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

13, 13, 24, 76, 169, 343, 741, 1618, 3451, 7390, 15924, 34201, 73387, 157681, 338754, 727483, 1562542, 3356380, 7209057, 15484111, 33258613, 71436250, 153437331, 329568094, 707879620, 1520453233, 3265779603, 7014566209, 15066579706
Offset: 1

Views

Author

R. H. Hardin, Apr 29 2018

Keywords

Comments

Column 6 of A303719.

Examples

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

Links

Crossrefs

Cf. A303719.

Formula

Empirical: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6) for n>9

A303718 Number of n X 7 0..1 arrays with every element unequal to 0, 1 or 5 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

21, 23, 40, 161, 361, 741, 1592, 3469, 7416, 15880, 34193, 73457, 157645, 338676, 727589, 1562584, 3356196, 7209121, 15484337, 33258365, 71436088, 153437805, 329568008, 707878984, 1520453793, 3265780153, 7014565013, 15066579716
Offset: 1

Views

Author

R. H. Hardin, Apr 29 2018

Keywords

Comments

Column 7 of A303719.

Examples

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

Links

Crossrefs

Cf. A303719.

Formula

Empirical: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6) for n>9
Showing 1-6 of 6 results.

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