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.

A280435 Number of nX3 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

1, 10, 21, 42, 77, 136, 236, 404, 687, 1162, 1959, 3294, 5528, 9262, 15497, 25898, 43233, 72100, 120132, 199992, 332675, 552970, 918491, 1524602, 2529072, 4192786, 6946941, 11503914, 19040117, 31497472, 52080284, 86073884, 142192983
Offset: 1

Views

Author

R. H. Hardin, Jan 03 2017

Keywords

Comments

Column 3 of A280440.

Examples

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

Links

Crossrefs

Cf. A280440.

Formula

Empirical: a(n) = 3*a(n-1) -a(n-2) -3*a(n-3) +a(n-4) +a(n-5) for n>6.
Empirical g.f.: x -x^2*(10-9*x-11*x^2+2*x^3) / ( (x-1)*(x^2+x-1)^2 ). - R. J. Mathar, Jan 04 2017

A280436 Number of nX4 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

2, 20, 42, 80, 138, 232, 386, 640, 1062, 1764, 2934, 4884, 8134, 13548, 22562, 37560, 62498, 103936, 172746, 286936, 476318, 790220, 1310222, 2171180, 3595918, 5952452, 9848346, 16286240, 26920122, 44477464, 73454354, 121259824, 200099094
Offset: 1

Views

Author

R. H. Hardin, Jan 03 2017

Keywords

Comments

Column 4 of A280440.

Examples

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

Links

Crossrefs

Cf. A280440.

Formula

Empirical: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>7.
Empirical g.f.: 2*x + 2*x^2*(10-19*x-4*x^2+13*x^3+x^5+2*x^4) / ( (x-1)^2*(x^2+x-1)^2 ). - R. J. Mathar, Jan 04 2017

A280437 Number of n X 5 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

5, 38, 77, 138, 225, 360, 574, 920, 1487, 2422, 3971, 6542, 10814, 17914, 29713, 49314, 81861, 135876, 225470, 373996, 620083, 1027598, 1702087, 2817898, 4662910, 7712270, 12749909, 21068730, 34800297, 57457632, 94828606, 156445952
Offset: 1

Views

Author

R. H. Hardin, Jan 03 2017

Keywords

Examples

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

Links

Crossrefs

Column 5 of A280440.

Formula

Empirical: a(n) = 4*a(n-1) - 4*a(n-2) - 2*a(n-3) + 4*a(n-4) - a(n-6) for n>7.
Empirical g.f.: x*(5 + 18*x - 55*x^2 - 8*x^3 + 37*x^4 + 14*x^5 + 7*x^6) / ((1 - x)^2*(1 - x - x^2)^2). - Colin Barker, Feb 13 2019

A280438 Number of n X 6 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

10, 68, 136, 232, 360, 548, 834, 1284, 2008, 3188, 5128, 8332, 13638, 22436, 37032, 61248, 101416, 168020, 278410, 461284, 764088, 1265228, 2094216, 3464892, 5730190, 9472388, 15651784, 25851544, 42680808, 70438148, 116203218, 191632452
Offset: 1

Views

Author

R. H. Hardin, Jan 03 2017

Keywords

Examples

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

Links

Crossrefs

Column 6 of A280440.

Formula

Empirical: a(n) = 4*a(n-1) - 4*a(n-2) - 2*a(n-3) + 4*a(n-4) - a(n-6) for n>7.
Empirical g.f.: 2*x*(5 + 14*x - 48*x^2 - 10*x^3 + 36*x^4 + 18*x^5 + 6*x^6) / ((1 - x)^2*(1 - x - x^2)^2). - Colin Barker, Feb 13 2019

A280439 Number of n X 7 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

20, 120, 236, 386, 574, 834, 1211, 1784, 2684, 4128, 6478, 10334, 16693, 27208, 44620, 73470, 121278, 200490, 331695, 548936, 908476, 1503260, 2486766, 4112326, 6797929, 11232984, 18554156, 30634874, 50561854, 83419218, 137578403
Offset: 1

Views

Author

R. H. Hardin, Jan 03 2017

Keywords

Examples

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

Links

Crossrefs

Column 7 of A280440.

Formula

Empirical: a(n) = 4*a(n-1) - 4*a(n-2) - 2*a(n-3) + 4*a(n-4) - a(n-6) for n>7.
Empirical g.f.: x*(20 + 40*x - 164*x^2 - 38*x^3 + 134*x^4 + 74*x^5 + 19*x^6) / ((1 - x)^2*(1 - x - x^2)^2). - Colin Barker, Feb 13 2019

A280434 Number of n X n 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 4, 21, 80, 225, 548, 1211, 2512, 4989, 9604, 18073, 33432, 61035, 110276, 197581, 351568, 621945
Offset: 1

Views

Author

R. H. Hardin, Jan 03 2017

Keywords

Comments

Diagonal of A280440.

Examples

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

Crossrefs

Cf. A280440.
Showing 1-6 of 6 results.

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