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A208269 T(n,k)=Number of nXk 0..1 arrays with new values 0..1 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 A208269 #7 Jul 22 2025 21:16:07
%S A208269 1,2,2,4,7,4,8,25,25,8,16,89,161,89,16,32,317,1033,1033,317,32,64,
%T A208269 1129,6631,11929,6631,1129,64,128,4021,42563,137845,137845,42563,4021,
%U A208269 128,256,14321,273205,1592731,2867739,1592731,273205,14321,256,512,51005,1753657
%N A208269 T(n,k)=Number of nXk 0..1 arrays with new values 0..1 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 A208269 Table starts
%C A208269 ...1.....2.......4.........8..........16............32..............64
%C A208269 ...2.....7......25........89.........317..........1129............4021
%C A208269 ...4....25.....161......1033........6631.........42563..........273205
%C A208269 ...8....89....1033.....11929......137845.......1592731........18403423
%C A208269 ..16...317....6631....137845.....2867739......59655167......1240971177
%C A208269 ..32..1129...42563...1592731....59655167....2234126207.....83670667271
%C A208269 ..64..4021..273205..18403423..1240971177...83670667271...5641457245533
%C A208269 .128.14321.1753657.212644499.25815151595.3133560234217.380372051615157
%H A208269 R. H. Hardin, <a href="/A208269/b208269.txt">Table of n, a(n) for n = 1..759</a>
%e A208269 Some solutions for n=4 k=3
%e A208269 ..0..1..0....0..0..1....0..0..0....0..1..0....0..0..0....0..0..0....0..0..0
%e A208269 ..0..0..0....0..1..0....0..1..1....1..0..1....0..1..1....1..0..1....1..0..1
%e A208269 ..1..1..1....1..1..1....1..0..1....0..0..0....1..0..1....0..1..1....1..0..1
%e A208269 ..1..0..0....0..0..0....0..1..0....1..1..0....0..1..1....0..0..1....1..0..1
%Y A208269 Column 2 is A007484(n-1)
%K A208269 nonn,tabl
%O A208269 1,2
%A A208269 _R. H. Hardin_ Feb 24 2012