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A240046 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

%I A240046 #11 Aug 04 2025 09:46:01
%S A240046 2,2,2,4,4,4,6,9,10,6,8,20,26,22,8,14,33,72,93,50,14,20,76,174,346,
%T A240046 309,119,20,30,117,597,1110,1496,1043,276,30,48,232,1187,5780,7514,
%U A240046 8567,3597,637,48,70,398,3115,17297,55034,61858,46381,12865,1473,70,108,675,7269
%N A240046 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.
%H A240046 R. H. Hardin, <a href="/A240046/b240046.txt">Table of n, a(n) for n = 1..126</a>
%H A240046 Esther Banaian, Elise Catania, Christian Gaetz, Miranda Moore, Gregg Musiker, and Kayla Wright, <a href="https://arxiv.org/abs/2507.15211">Twists, Higher Dimer Covers, and Web Duality for Grassmannian Cluster Algebras</a>, arXiv:2507.15211 [math.CO], 2025. See p. 28.
%F A240046 Empirical for column k:
%F A240046 k=1: a(n) = a(n-2) +2*a(n-3)
%F A240046 k=2: [order 38] for n>40
%F A240046 Empirical for row n:
%F A240046 n=1: a(n) = a(n-2) +2*a(n-3)
%F A240046 n=2: [order 18] for n>22
%F A240046 n=3: [order 76] for n>96
%e A240046 Table starts
%e A240046 ..2....2......4.......6.........8..........14..........20..........30
%e A240046 ..2....4......9......20........33..........76.........117.........232
%e A240046 ..4...10.....26......72.......174.........597........1187........3115
%e A240046 ..6...22.....93.....346......1110........5780.......17297.......57800
%e A240046 ..8...50....309....1496......7514.......55034......236282.....1248277
%e A240046 .14..119...1043....8567.....61858......640643.....4593632....35084947
%e A240046 .20..276...3597...46381....515675.....8300260...104619164..1204711882
%e A240046 .30..637..12865..268672...4743056...119956268..2789729009.49892724623
%e A240046 .48.1473..45491.1556758..45158204..1944727891.80805084589
%e A240046 .70.3355.163686.9438166.453408919.34311716212
%e A240046 Some solutions for n=3 k=4
%e A240046 ..2..3..2..2....3..2..2..2....2..3..3..3....2..3..2..2....2..3..3..3
%e A240046 ..3..1..1..0....2..0..0..0....3..1..2..0....3..1..1..3....3..1..1..2
%e A240046 ..3..1..2..3....2..0..0..0....2..1..2..0....2..1..1..2....3..2..2..2
%Y A240046 Row and Column 1 are A239851
%K A240046 nonn,tabl
%O A240046 1,1
%A A240046 _R. H. Hardin_, Mar 31 2014