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%I #16 Jun 28 2017 02:35:57
%S 1,4,4,16,52,16,64,676,676,64,256,8788,28564,8788,256,1024,114244,
%T 1206964,1206964,114244,1024,4096,1485172,50999956,165770032,50999956,
%U 1485172,4096,16384,19307236,2154990196,22767656980,22767656980
%N T(n,k) = number of n X k 0..4 arrays with no entry increasing mod 5 by 4 rightwards or downwards, starting with upper left zero.
%C 1/5 the number of 5-colorings of the grid graph P_n X P_k. - _Andrew Howroyd_, Jun 26 2017
%H Andrew Howroyd, <a href="/A222144/b222144.txt">Table of n, a(n) for n = 1..378</a> (terms 1..127 from R. H. Hardin)
%F T(n,k) = 4 * (6*A198906(n,k) - 3*A207997(n,k) - 2) for n*k > 1. - _Andrew Howroyd_, Jun 27 2017
%e Table starts
%e .......1.............4...................16.........................64
%e .......4............52..................676.......................8788
%e ......16...........676................28564....................1206964
%e ......64..........8788..............1206964..................165770032
%e .....256........114244.............50999956................22767656980
%e ....1024.......1485172...........2154990196..............3127020364012
%e ....4096......19307236..........91058563924............429480137694664
%e ...16384.....250994068........3847656513844..........58986884432558548
%e ...65536....3262922884......162581749707796........8101544704688334244
%e ..262144...42417997492.....6869850581244916.....1112705429924911477552
%e .1048576..551433967396...290283793189916884...152824358676750267429220
%e .4194304.7168641576148.12265868026121849524.20989638386627725143014812
%e ...
%e Some solutions for n=3, k=4:
%e ..0..0..1..1....0..0..0..0....0..0..0..0....0..0..0..0....0..0..1..1
%e ..1..1..2..2....1..1..1..2....0..1..3..3....0..2..2..0....0..1..2..3
%e ..3..4..0..0....1..3..1..3....2..2..0..1....0..2..2..2....1..4..2..3
%Y Columns 1-7 are A000302(n-1), A222138, A222139, A222140, A222141, A222142, A222143.
%Y Main diagonal is A068255.
%Y Cf. A078099 (3 colorings), A222444 (4 colorings), A198906 (unlabeled 5 colorings), A222281 (6 colorings), A222340 (7 colorings), A222462 (8 colorings).
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Feb 09 2013
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