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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.

%I A202471 #21 Jul 08 2025 10:46:47
%S A202471 265,1573,1573,9253,16561,9253,54085,172197,172197,54085,317179,
%T A202471 1774281,3157010,1774281,317179,1858993,18374521,57262144,57262144,
%U A202471 18374521,1858993,10894297,190112777,1044865367,1828904402,1044865367,190112777,10894297
%N 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.
%H A202471 Liang Kai, <a href="/A202471/b202471.txt">Table of n, a(n) for n = 1..465</a> (first 241 terms from R. H. Hardin)
%e A202471 Table starts
%e A202471 ......265........1573..........9253............54085.............317179
%e A202471 .....1573.......16561........172197..........1774281...........18374521
%e A202471 .....9253......172197.......3157010.........57262144.........1044865367
%e A202471 ....54085.....1774281......57262144.......1828904402........58746383721
%e A202471 ...317179....18374521....1044865367......58746383721......3323590649777
%e A202471 ..1858993...190112777...19045287529....1885066867201....187820723381421
%e A202471 .10894297..1966463785..347030298362...60472625443366..10610932604054547
%e A202471 .63850777.20345296193.6325139804762.1940390570621922.599616560193259281
%e A202471 ...
%e A202471 Some solutions for n=1, k=3
%e A202471 ..0..1..1..0..1....0..1..0..1..0....0..0..0..0..0....1..1..0..1..0
%e A202471 ..0..0..1..0..0....1..0..0..0..1....1..0..0..1..0....1..1..0..0..0
%e A202471 ..0..0..0..0..1....1..1..0..1..0....0..1..0..0..0....0..0..0..0..1
%Y A202471 Diagonal is A050974(n+2), col/row 1 is A202464, col/row 2 is A202465, col/row 3 is A202466.
%K A202471 nonn,tabl
%O A202471 1,1
%A A202471 _R. H. Hardin_, Dec 19 2011