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A195978 T(n,k) = Number of n X k 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 2,0,1,3,4 for x=0,1,2,3,4.

%I A195978 #7 Oct 29 2022 15:13:06
%S A195978 1,3,3,4,9,4,5,14,14,5,9,23,24,23,9,16,43,36,36,43,16,25,78,67,67,67,
%T A195978 78,25,39,139,134,133,133,134,139,39,64,249,240,256,244,256,240,249,
%U A195978 64,105,450,432,455,519,519,455,432,450,105,169,815,803,931,1072,1280,1072,931
%N A195978 T(n,k) = Number of n X k 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 2,0,1,3,4 for x=0,1,2,3,4.
%C A195978 Every 0 is next to 0 2's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 3's, every 4 is next to 4 4's.
%C A195978 Table starts
%C A195978 ...1...3....4....5....9....16....25.....39.....64.....105.....169......272
%C A195978 ...3...9...14...23...43....78...139....249....450.....815....1475.....2674
%C A195978 ...4..14...24...36...67...134...240....432....803....1501....2764.....5118
%C A195978 ...5..23...36...67..133...256...455....931...1830....3565....7001....13872
%C A195978 ...9..43...67..133..244...519..1072...2225...4456....9098...19066....39689
%C A195978 ..16..78..134..256..519..1280..2718...5830..12799...28969...64536...144480
%C A195978 ..25.139..240..455.1072..2718..5637..12823..30486...72042..166884...390514
%C A195978 ..39.249..432..931.2225..5830.12823..32909..82310..202795..499687..1270420
%C A195978 ..64.450..803.1830.4456.12799.30486..82310.212185..562730.1497281..4025955
%C A195978 .105.815.1501.3565.9098.28969.72042.202795.562730.1609756.4534710.12951901
%H A195978 R. H. Hardin, <a href="/A195978/b195978.txt">Table of n, a(n) for n = 1..311</a>
%e A195978 Some solutions for n=6, k=4
%e A195978 ..0..1..1..0....0..0..1..2....2..1..0..1....0..1..1..1....0..1..1..0
%e A195978 ..1..1..1..1....0..0..1..1....1..1..0..1....1..1..0..0....0..1..1..1
%e A195978 ..1..0..0..1....1..1..1..0....0..1..1..1....2..1..0..0....1..1..0..1
%e A195978 ..2..1..1..1....1..1..1..1....0..1..1..0....2..1..0..0....1..1..0..1
%e A195978 ..2..1..1..0....0..0..0..1....0..1..1..0....1..1..1..1....0..1..1..1
%e A195978 ..1..0..1..1....0..0..0..1....1..2..2..1....0..0..1..2....0..1..1..0
%K A195978 nonn,tabl
%O A195978 1,2
%A A195978 _R. H. Hardin_, Sep 25 2011