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 1-4 of 4 results.

A231134 Number of (n+1) X (2+1) black-square subarrays of 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

2, 9, 40, 182, 808, 3688, 16368, 74728, 331648, 1514160, 6719936, 30680320, 136161152, 621652928, 2758934016, 12596099456, 55902265856, 255225567744, 1132706802688, 5171449356800, 22951211032576, 104785303002112
Offset: 1

Views

Author

R. H. Hardin, Nov 04 2013

Keywords

Examples

			Some solutions for n=5:
..x..0..x....x..0..x....x..0..x....x..0..x....x..0..x....x..0..x....x..0..x
..1..x..2....1..x..0....1..x..2....1..x..1....0..x..1....0..x..1....1..x..2
..x..1..x....x..2..x....x..1..x....x..2..x....x..1..x....x..2..x....x..0..x
..0..x..0....0..x..0....0..x..1....1..x..1....2..x..0....2..x..0....1..x..2
..x..1..x....x..2..x....x..0..x....x..2..x....x..2..x....x..1..x....x..0..x
..2..x..0....1..x..0....2..x..2....0..x..0....0..x..0....2..x..0....2..x..2
		

Crossrefs

Column 2 of A231137.

Formula

Empirical: a(n) = 22*a(n-2) - 36*a(n-4) + 16*a(n-6).
Empirical g.f.: x*(2 + 9*x - 4*x^2 - 16*x^3 + 8*x^5) / (1 - 22*x^2 + 36*x^4 - 16*x^6). - Colin Barker, Sep 26 2018

A231135 Number of (n+1)X(4+1) black-square subarrays of 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

16, 182, 2260, 27171, 336004, 4066129, 50257244, 608468617, 7520563372, 91054483047, 1125418461348, 13625913937795, 168414092245220, 2039060342079409, 25202456511185596, 305136757252909097
Offset: 1

Views

Author

R. H. Hardin, Nov 04 2013

Keywords

Comments

Column 4 of A231137

Examples

			Some solutions for n=4
..x..0..x..1..x....x..0..x..1..x....x..0..x..1..x....x..0..x..0..x
..0..x..2..x..0....1..x..0..x..2....2..x..0..x..1....0..x..1..x..2
..x..1..x..0..x....x..2..x..2..x....x..2..x..0..x....x..2..x..2..x
..1..x..1..x..1....0..x..1..x..0....1..x..1..x..2....1..x..1..x..1
..x..2..x..0..x....x..0..x..2..x....x..2..x..1..x....x..2..x..0..x
		

Formula

Empirical: a(n) = 175*a(n-2) -4017*a(n-4) +34311*a(n-6) -146236*a(n-8) +322472*a(n-10) -291040*a(n-12) +116032*a(n-14) -24064*a(n-16) +1024*a(n-18)

A231136 Number of (n+1)X(6+1) black-square subarrays of 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

120, 3688, 124644, 4066129, 137063228, 4509445997, 151928497692, 5001540387953, 168507419403536, 5547511896771810, 186902346005124780, 6153112021568081647, 207305819737090195456, 6824826623169051569950, 229936709033952423239528
Offset: 1

Views

Author

R. H. Hardin, Nov 04 2013

Keywords

Comments

Column 6 of A231137

Examples

			Some solutions for n=2
..x..0..x..1..x..1..x....x..0..x..1..x..1..x....x..0..x..1..x..0..x
..1..x..2..x..2..x..0....1..x..0..x..1..x..0....0..x..2..x..2..x..2
..x..2..x..0..x..1..x....x..2..x..2..x..2..x....x..1..x..1..x..0..x
		

Formula

Empirical recurrence of order 90 (see link above)

A231133 Number of (n+1)X(n+1) black-square subarrays of 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

1, 9, 308, 27171, 6794904, 4509445997, 8349491299560, 41122867660973690, 564457878709147238868, 20611335365445954476620968, 2097381737046509117354544061212, 567772314049031950964995256826728363
Offset: 1

Views

Author

R. H. Hardin, Nov 04 2013

Keywords

Comments

Diagonal of A231137

Examples

			Some solutions for n=4
..x..0..x..1..x....x..0..x..1..x....x..0..x..0..x....x..0..x..0..x
..2..x..0..x..2....1..x..2..x..2....1..x..0..x..1....0..x..1..x..2
..x..0..x..1..x....x..0..x..0..x....x..1..x..1..x....x..2..x..1..x
..1..x..0..x..0....2..x..1..x..2....0..x..2..x..0....1..x..2..x..1
..x..2..x..1..x....x..0..x..1..x....x..2..x..2..x....x..0..x..0..x
		
Showing 1-4 of 4 results.