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%I #4 Dec 22 2014 20:33:39
%S 1305,15395,24951,175204,510488,488880,2045858,10339272,17431462,
%T 9644050,23788014,211956317,610768407,598576435,190273279,277324636,
%U 4399478503,21483285845,36248318755,20541757032,3754660940,3231587589,91508212229
%N T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every consecutive three elements in every row and diagonal having one or two distinct values, and in every column and antidiagonal having two or three distinct values, and new values 0 upwards introduced in row major order
%C Table starts
%C ..........1305..........15395..........175204.........2045858........23788014
%C .........24951.........510488........10339272.......211956317......4399478503
%C ........488880.......17431462.......610768407.....21483285845....777477410236
%C .......9644050......598576435.....36248318755...2207250617866.140063220191585
%C .....190273279....20541757032...2154288643145.227032633146768
%C ....3754660940...705111416679.127991617429929
%C ...74090662687.24203999575311
%C .1462043624070
%H R. H. Hardin, <a href="/A252844/b252844.txt">Table of n, a(n) for n = 1..39</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 52] for n>53
%F Empirical for row n:
%F n=1: [linear recurrence of order 96] for n>99
%e Some solutions for n=1 k=4
%e ..0..0..1..1..2..1....0..0..1..1..2..2....0..0..0..0..1..0....0..0..1..1..1..2
%e ..0..0..3..3..2..3....2..0..0..3..3..1....2..0..0..1..0..1....1..0..1..1..0..0
%e ..1..1..0..0..1..1....0..2..2..1..1..3....1..2..2..1..1..2....3..3..0..0..0..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 22 2014
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