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Number of nX1 0..5 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other
+10
2
6, 15, 33, 46, 44, 20, 214, 1055, 3020, 5124, 4965, 2136, 27564, 156000, 491176, 899572, 909040, 394760, 5486260, 32803375, 107532655, 203115730, 209292900, 91748000, 1319324175, 8093115065, 27032377190, 51739373280, 53721457020
EXAMPLE
Some solutions for n=3
..0....3....1....1....2....0....3....0....2....1....2....0....0....1....0....1
..1....4....5....3....4....4....5....3....3....3....5....3....4....4....1....2
..2....5....4....5....5....5....4....4....5....4....4....2....3....5....3....3
Number of nX2 0..5 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other
+10
1
15, 30, 13, 649, 3247, 1483, 84463, 395138, 147370, 10892006, 61376744, 26060323, 1860718688, 9722469665, 3689916515, 298977508446, 1746612244800, 731620635705, 56300135952299, 307084986199367, 118048036603381
EXAMPLE
Some solutions for n=3
..0..1....0..2....0..3....0..1....0..2....0..3....0..3....0..2....0..1....0..3
..2..3....1..4....1..4....2..5....1..5....2..4....2..5....1..3....3..5....1..5
..4..5....3..5....2..5....3..4....3..4....1..5....1..4....4..5....2..4....2..4
Number of n X n 0..5 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.
+10
0
6, 30, 1848, 352339, 218373106
EXAMPLE
Some solutions for n=3:
..0..1..2....0..3..2....0..2..1....0..0..2....0..3..2....0..2..3....0..3..2
..0..4..4....0..3..4....0..5..5....1..3..4....1..5..4....2..4..3....1..5..5
..3..5..5....1..5..5....1..4..3....1..5..5....2..4..3....1..4..5....1..4..4
Number of nX3 0..5 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other
+10
0
33, 13, 1848, 1329, 219302, 142698, 28966191, 19687441, 4250955750, 2868249876, 653092745412, 444880771844, 102659474241588, 68568844067091
EXAMPLE
Some solutions for n=4
..0..2..2....0..0..2....0..0..1....0..0..4....0..0..2....0..0..3....0..2..4
..0..4..3....1..3..4....2..3..3....1..2..4....1..4..3....1..1..3....0..2..4
..1..3..4....1..5..4....1..2..4....1..2..5....1..5..3....4..5..5....1..3..5
..1..5..5....2..3..5....4..5..5....3..3..5....2..5..4....2..2..4....1..3..5
Number of nX4 0..5 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other
+10
0
46, 649, 1329, 352339, 8982755, 18172239, 6469118415, 184228587259, 391072885802
EXAMPLE
Some solutions for n=3
..0..0..2..1....0..0..1..2....0..0..2..1....0..0..1..1....0..2..1..1
..1..3..5..5....1..3..3..4....2..4..5..4....2..2..5..3....0..3..2..5
..2..3..4..4....2..5..5..4....1..3..5..3....3..5..4..4....3..4..4..5
Number of nX5 0..5 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other
+10
0
44, 3247, 219302, 8982755, 218373106, 2162004143, 784706456797
EXAMPLE
Some solutions for n=3
..0..0..0..3..2....0..0..2..1..3....0..0..0..3..3....0..0..0..2..3
..1..2..2..5..3....0..2..4..3..4....1..1..4..4..5....1..1..2..5..3
..1..4..5..4..4....1..3..5..4..5....2..2..5..5..4....2..5..4..4..4
Number of nX6 0..5 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other
+10
0
20, 1483, 142698, 18172239, 2162004143
EXAMPLE
Some solutions for n=3
..0..0..1..3..1..2....0..0..0..1..1..2....0..0..0..1..2..1....0..0..0..1..2..1
..0..2..3..3..2..5....2..2..3..3..4..4....1..3..2..4..4..5....2..2..5..3..4..5
..1..5..4..4..4..5....1..5..3..5..5..4....2..4..3..3..5..5....1..3..3..5..4..4
Number of nX7 0..5 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other
+10
0
214, 84463, 28966191, 6469118415, 784706456797
EXAMPLE
Some solutions for n=2
..0..1..2..3..2..3..4....0..0..0..2..3..2..2....0..0..3..1..1..3..3
..0..1..5..4..4..5..5....1..1..3..5..5..4..4....2..2..5..5..4..4..5
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