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A229412 T(n,k)=Number of nXk 0..3 arrays avoiding 11 horizontally, 22 vertically, 33 antidiagonally and 00 diagonally.

%I A229412 #6 Jul 23 2025 05:43:46
%S A229412 4,15,15,57,163,57,216,1756,1756,216,819,18712,53538,18712,819,3105,
%T A229412 199595,1629298,1629298,199595,3105,11772,2127718,49788258,142475606,
%U A229412 49788258,2127718,11772,44631,22684613,1519840402,12462062342
%N A229412 T(n,k)=Number of nXk 0..3 arrays avoiding 11 horizontally, 22 vertically, 33 antidiagonally and 00 diagonally.
%C A229412 Table starts
%C A229412 .....4........15............57..............216..................819
%C A229412 ....15.......163..........1756............18712...............199595
%C A229412 ....57......1756.........53538..........1629298.............49788258
%C A229412 ...216.....18712.......1629298........142475606..........12462062342
%C A229412 ...819....199595......49788258......12462062342........3113479414050
%C A229412 ..3105...2127718....1519840402....1088122273732......777638567093963
%C A229412 .11772..22684613...46408035676...95053083585891...194334416016079648
%C A229412 .44631.241841143.1416912709750.8301763765531574.48554820719187209670
%H A229412 R. H. Hardin, <a href="/A229412/b229412.txt">Table of n, a(n) for n = 1..220</a>
%F A229412 Empirical for column k:
%F A229412 k=1: a(n) = 3*a(n-1) +3*a(n-2)
%F A229412 k=2: a(n) = 10*a(n-1) +13*a(n-2) -67*a(n-3) +38*a(n-4) -2*a(n-5)
%F A229412 k=3: [order 13]
%F A229412 k=4: [order 40]
%e A229412 Some solutions for n=3 k=4
%e A229412 ..0..0..0..3....0..2..0..2....0..0..3..0....0..0..2..2....0..0..3..0
%e A229412 ..3..2..2..2....0..1..0..1....0..2..1..0....3..3..1..3....2..2..2..1
%e A229412 ..3..0..1..3....0..2..3..3....2..3..0..3....1..3..2..0....0..0..1..3
%Y A229412 Column 1 is A125145
%K A229412 nonn,tabl
%O A229412 1,1
%A A229412 _R. H. Hardin_ Sep 22 2013