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.

Previous Showing 11-13 of 13 results.

A281210 Number of 6 X n 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 420, 1120, 1588, 2602, 4248, 6838, 11010, 17840, 29120, 47838, 78978, 130842, 217250, 361188, 600860, 999718, 1663078, 2765630, 4596962, 7636856, 12679768, 21040526, 34894090, 57836514, 95810754, 158634028, 262516660, 434214550
Offset: 1

Views

Author

R. H. Hardin, Jan 17 2017

Keywords

Examples

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

Links

Crossrefs

Row 6 of A281205.

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>12.
Empirical g.f.: 2*x^2*(210 - 280*x - 606*x^2 + 785*x^3 + 376*x^4 - 525*x^5 - 39*x^6 + 180*x^7 + 36*x^8 - 6*x^9 - 3*x^10) / ((1 - x)^2*(1 - x - x^2)^2). - Colin Barker, Feb 18 2019

A281211 Number of 7 X n 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 1308, 2688, 3604, 5712, 9118, 14375, 22700, 36144, 58168, 94524, 154800, 254959, 421560, 698756, 1159898, 1926760, 3201376, 5318733, 8833940, 14666360, 24337820, 40366132, 66914912, 110866187, 183590176, 303864300, 502685950, 831204864
Offset: 1

Views

Author

R. H. Hardin, Jan 17 2017

Keywords

Examples

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

Links

Crossrefs

Row 7 of A281205.

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>13.
Empirical g.f.: x^2*(1308 - 2544*x - 1916*x^2 + 4664*x^3 + 830*x^4 - 2793*x^5 - 12*x^6 + 920*x^7 + 274*x^8 + 40*x^9 - 18*x^10 - 10*x^11) / ((1 - x)^2*(1 - x - x^2)^2). - Colin Barker, Feb 18 2019

A281198 Number of n X n 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

0, 2, 56, 270, 1141, 4248, 14375, 45614, 138676, 409976, 1190740, 3421202, 9767347, 27782656, 78849645
Offset: 1

Views

Author

R. H. Hardin, Jan 17 2017

Keywords

Comments

Diagonal of A281205.

Examples

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

Crossrefs

Cf. A281205.
Previous Showing 11-13 of 13 results.

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