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A222169 T(n,k)=Number of nXk 0..4 arrays with entries increasing mod 5 by 0, 1 or 2 rightwards and downwards, starting with upper left zero.

%I A222169 #6 Jul 23 2025 02:27:01
%S A222169 1,3,3,9,19,9,27,121,121,27,81,771,1665,771,81,243,4913,22979,22979,
%T A222169 4913,243,729,31307,317259,690437,317259,31307,729,2187,199497,
%U A222169 4380445,20780181,20780181,4380445,199497,2187,6561,1271251,60481881,625649047
%N A222169 T(n,k)=Number of nXk 0..4 arrays with entries increasing mod 5 by 0, 1 or 2 rightwards and downwards, starting with upper left zero.
%C A222169 Table starts
%C A222169 ......1..........3..............9.................27.....................81
%C A222169 ......3.........19............121................771...................4913
%C A222169 ......9........121...........1665..............22979.................317259
%C A222169 .....27........771..........22979.............690437...............20780181
%C A222169 .....81.......4913.........317259...........20780181.............1366395515
%C A222169 ....243......31307........4380445..........625649047............89948464453
%C A222169 ....729.....199497.......60481881........18838482047..........5923189816253
%C A222169 ...2187....1271251......835088891.......567241901289........390086038882651
%C A222169 ...6561....8100769....11530288395.....17080173559277......25690815631493191
%C A222169 ..19683...51620379...159201677509....514300085627023....1691995329032459285
%C A222169 ..59049..328939577..2198138788809..15486061794514775..111434983000652039093
%C A222169 .177147.2096095523.30350271502115.466299978310573033.7339124863989795685471
%H A222169 R. H. Hardin, <a href="/A222169/b222169.txt">Table of n, a(n) for n = 1..180</a>
%F A222169 Empirical for column k:
%F A222169 k=1: a(n) = 3*a(n-1)
%F A222169 k=2: a(n) = 7*a(n-1) -4*a(n-2)
%F A222169 k=3: a(n) = 16*a(n-1) -31*a(n-2) +10*a(n-3)
%F A222169 k=4: [order 10]
%F A222169 k=5: [order 25]
%F A222169 k=6: [order 70]
%e A222169 Some solutions for n=3 k=4
%e A222169 ..0..1..3..3....0..2..3..3....0..1..2..4....0..1..3..4....0..0..0..1
%e A222169 ..2..3..0..0....0..2..4..4....1..2..3..4....1..3..4..1....0..2..2..2
%e A222169 ..4..0..0..0....2..4..4..0....1..2..3..4....3..4..4..1....0..2..2..3
%Y A222169 Diagonal is A068748
%Y A222169 Column 1 is A000244(n-1)
%Y A222169 Column 2 is A138977
%Y A222169 Column 3 is A138978
%Y A222169 Column 4 is A138979
%K A222169 nonn,tabl
%O A222169 1,2
%A A222169 _R. H. Hardin_ Feb 10 2013