A050974 -id:A050974 - cp's OEIS frontend

A202471 T(n,k) = Number of (n+2) X (k+2) binary arrays with no more than two of any consecutive three bits set in any row or column.

265, 1573, 1573, 9253, 16561, 9253, 54085, 172197, 172197, 54085, 317179, 1774281, 3157010, 1774281, 317179, 1858993, 18374521, 57262144, 57262144, 18374521, 1858993, 10894297, 190112777, 1044865367, 1828904402, 1044865367, 190112777, 10894297

Offset: 1

R. H. Hardin, Dec 19 2011

			Table starts
......265........1573..........9253............54085.............317179
.....1573.......16561........172197..........1774281...........18374521
.....9253......172197.......3157010.........57262144.........1044865367
....54085.....1774281......57262144.......1828904402........58746383721
...317179....18374521....1044865367......58746383721......3323590649777
..1858993...190112777...19045287529....1885066867201....187820723381421
.10894297..1966463785..347030298362...60472625443366..10610932604054547
.63850777.20345296193.6325139804762.1940390570621922.599616560193259281
...
Some solutions for n=1, k=3
..0..1..1..0..1....0..1..0..1..0....0..0..0..0..0....1..1..0..1..0
..0..0..1..0..0....1..0..0..0..1....1..0..0..1..0....1..1..0..0..0
..0..0..0..0..1....1..1..0..1..0....0..1..0..0..0....0..0..0..0..1

Liang Kai, Table of n, a(n) for n = 1..465 (first 241 terms from R. H. Hardin)

Diagonal is A050974(n+2), col/row 1 is A202464, col/row 2 is A202465, col/row 3 is A202466.

A067968 Number of binary arrangements on n X n array without adjacent three 1's.

Original entry on oeis.org

1, 2, 11, 163, 6547, 720417, 216173426, 177509416175, 398239490006383, 2441922679051541299, 40923800121824894177005, 1874434223405139511637099884, 234647514833189124245764389957097, 80281172893810827268371440460572492150

Offset: 0

R. H. Hardin, Feb 02 2002

nonn

Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 342-349.

Steven R. Finch, Hard Square Entropy Constant [Broken link]
Steven R. Finch, Hard Square Entropy Constant [From the Wayback machine]

Adjacent three in a row or column gives A050974.

a(13) from Sean A. Irvine, Jan 15 2024

a(0)=1 prepended by Alois P. Heinz, Sep 26 2024

cp's OEIS Frontend

A202471 T(n,k) = Number of (n+2) X (k+2) binary arrays with no more than two of any consecutive three bits set in any row or column.

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