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A208864 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 one of its immediate leftward or upward or left-upward diagonal neighbors.

%I A208864 #7 Jul 22 2025 21:32:12
%S A208864 1,2,2,5,11,5,15,127,127,15,51,1691,5796,1691,51,187,23047,273049,
%T A208864 273049,23047,187,715,315203,12883280,44452082,12883280,315203,715,
%U A208864 2795,4313071,607924387,7240366702,7240366702,607924387,4313071,2795,11051,59022155
%N A208864 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 one of its immediate leftward or upward or left-upward diagonal neighbors.
%C A208864 Table starts
%C A208864 ....1........2.............5................15....................51
%C A208864 ....2.......11...........127..............1691.................23047
%C A208864 ....5......127..........5796............273049..............12883280
%C A208864 ...15.....1691........273049..........44452082............7240366702
%C A208864 ...51....23047......12883280........7240366702.........4071491223248
%C A208864 ..187...315203.....607924387.....1179377179523......2289701830963879
%C A208864 ..715..4313071...28686344276...192108983085145...1287681340443915644
%C A208864 .2795.59022155.1353633375649.31292693945057258.724166398812363542260
%H A208864 R. H. Hardin, <a href="/A208864/b208864.txt">Table of n, a(n) for n = 1..144</a>
%e A208864 Some solutions for n=4 k=3
%e A208864 ..0..0..1....0..0..0....0..1..1....0..1..0....0..0..0....0..0..0....0..0..0
%e A208864 ..0..2..0....0..1..2....1..0..2....0..2..3....0..1..2....0..1..1....0..1..1
%e A208864 ..1..2..1....1..2..3....3..0..1....3..0..0....2..1..2....0..1..2....1..2..0
%e A208864 ..3..0..0....1..0..0....1..1..2....2..1..3....0..1..2....2..3..2....1..0..1
%Y A208864 Column 1 is A007581(n-1)
%K A208864 nonn,tabl
%O A208864 1,2
%A A208864 _R. H. Hardin_ Mar 02 2012