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A196809 T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,2,3,0,1 for x=0,1,2,3,4.

%I A196809 #7 Jun 02 2025 04:34:51
%S A196809 1,1,1,1,1,1,1,3,3,1,1,7,16,7,1,1,17,37,37,17,1,1,41,120,193,120,41,1,
%T A196809 1,99,420,1515,1515,420,99,1,1,239,1468,8719,19449,8719,1468,239,1,1,
%U A196809 577,4801,52291,166682,166682,52291,4801,577,1,1,1393,15885,334317,1730105
%N A196809 T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,2,3,0,1 for x=0,1,2,3,4.
%C A196809 Every 0 is next to 0 4's, every 1 is next to 1 2's, every 2 is next to 2 3's, every 3 is next to 3 0's, every 4 is next to 4 1's
%C A196809 Table starts
%C A196809 .1....1.....1........1..........1............1..............1................1
%C A196809 .1....1.....3........7.........17...........41.............99..............239
%C A196809 .1....3....16.......37........120..........420...........1468.............4801
%C A196809 .1....7....37......193.......1515.........8719..........52291...........334317
%C A196809 .1...17...120.....1515......19449.......166682........1730105.........18344433
%C A196809 .1...41...420.....8719.....166682......2535368.......46685074........822353649
%C A196809 .1...99..1468....52291....1730105.....46685074.....1436535356......42144649101
%C A196809 .1..239..4801...334317...18344433....822353649....42144649101....2099296647197
%C A196809 .1..577.15885..2067173..186996068..14219232895..1242942835600..105892691714203
%C A196809 .1.1393.53128.12663609.1929020093.247793610490.36966191677933.5317907954180181
%H A196809 R. H. Hardin, <a href="/A196809/b196809.txt">Table of n, a(n) for n = 1..220</a>
%e A196809 Some solutions for n=6 k=4
%e A196809 ..0..0..0..0....0..0..0..0....0..3..0..0....0..0..3..0....0..3..0..0
%e A196809 ..0..3..0..3....0..3..2..0....3..0..3..0....0..0..0..0....0..0..0..0
%e A196809 ..0..2..1..0....3..0..3..0....0..0..3..0....0..0..1..0....3..0..0..0
%e A196809 ..0..3..0..0....0..3..0..0....3..0..0..0....0..3..2..1....0..3..0..3
%e A196809 ..3..0..0..0....0..2..3..0....0..0..0..0....0..0..3..0....1..2..3..0
%e A196809 ..0..3..0..0....0..0..0..0....0..3..0..0....0..3..0..0....0..1..0..0
%Y A196809 Column 2 is A001333(n-1)
%K A196809 nonn,tabl
%O A196809 1,8
%A A196809 _R. H. Hardin_ Oct 06 2011