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.
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, 309, 119, 20, 30, 117, 597, 1110, 1496, 1043, 276, 30, 48, 232, 1187, 5780, 7514, 8567, 3597, 637, 48, 70, 398, 3115, 17297, 55034, 61858, 46381, 12865, 1473, 70, 108, 675, 7269
Offset: 1
Examples
Table starts ..2....2......4.......6.........8..........14..........20..........30 ..2....4......9......20........33..........76.........117.........232 ..4...10.....26......72.......174.........597........1187........3115 ..6...22.....93.....346......1110........5780.......17297.......57800 ..8...50....309....1496......7514.......55034......236282.....1248277 .14..119...1043....8567.....61858......640643.....4593632....35084947 .20..276...3597...46381....515675.....8300260...104619164..1204711882 .30..637..12865..268672...4743056...119956268..2789729009.49892724623 .48.1473..45491.1556758..45158204..1944727891.80805084589 .70.3355.163686.9438166.453408919.34311716212 Some solutions for n=3 k=4 ..2..3..2..2....3..2..2..2....2..3..3..3....2..3..2..2....2..3..3..3 ..3..1..1..0....2..0..0..0....3..1..2..0....3..1..1..3....3..1..1..2 ..3..1..2..3....2..0..0..0....2..1..2..0....2..1..1..2....3..2..2..2
Links
- R. H. Hardin, Table of n, a(n) for n = 1..126
- Esther Banaian, Elise Catania, Christian Gaetz, Miranda Moore, Gregg Musiker, and Kayla Wright, Twists, Higher Dimer Covers, and Web Duality for Grassmannian Cluster Algebras, arXiv:2507.15211 [math.CO], 2025. See p. 28.
Crossrefs
Row and Column 1 are A239851
Formula
Empirical for column k:
k=1: a(n) = a(n-2) +2*a(n-3)
k=2: [order 38] for n>40
Empirical for row n:
n=1: a(n) = a(n-2) +2*a(n-3)
n=2: [order 18] for n>22
n=3: [order 76] for n>96