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A208201 T(n,k)=Number of nXk 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or left-upward diagonal neighbors.

%I A208201 #7 Jul 22 2025 21:14:46
%S A208201 1,2,2,5,14,5,15,178,178,15,51,2653,10366,2653,51,187,41272,639701,
%T A208201 639701,41272,187,715,648569,39725054,156617480,39725054,648569,715,
%U A208201 2795,10215440,2468504665,38372808893,38372808893,2468504665,10215440,2795
%N A208201 T(n,k)=Number of nXk 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or left-upward diagonal neighbors.
%C A208201 Table starts
%C A208201 ....1.........2.............5.................15......................51
%C A208201 ....2........14...........178...............2653...................41272
%C A208201 ....5.......178.........10366.............639701................39725054
%C A208201 ...15......2653........639701..........156617480.............38372808893
%C A208201 ...51.....41272......39725054........38372808893..........37069738362057
%C A208201 ..187....648569....2468504665......9402035642924.......35810971705853725
%C A208201 ..715..10215440..153402542384...2303673397508915....34594950233928279876
%C A208201 .2795.160984657.9533100532733.564442821781056268.33420220819293699707599
%H A208201 R. H. Hardin, <a href="/A208201/b208201.txt">Table of n, a(n) for n = 1..220</a>
%e A208201 Some solutions for n=4 k=3
%e A208201 ..0..0..1....0..0..0....0..1..1....0..0..0....0..1..1....0..0..0....0..1..0
%e A208201 ..0..2..0....0..1..1....0..0..0....1..1..0....1..0..0....0..1..2....0..2..3
%e A208201 ..1..2..1....2..0..2....0..1..1....0..1..0....0..1..0....1..1..3....3..0..0
%e A208201 ..3..0..0....2..1..0....0..2..1....0..1..0....1..0..0....1..0..0....2..1..3
%Y A208201 Column 1 is A007581(n-1)
%K A208201 nonn,tabl
%O A208201 1,2
%A A208201 _R. H. Hardin_ Feb 24 2012