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Number of 4 X 4 0..n arrays with row and column sums one greater than the previous row and column.

0

`%I #6 Apr 30 2022 21:04:58
`

`%S 2,1346,41852,491892,3436102,17232446,68544440,229551288,672922218,
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`%T 1773763178,4286374004,9634559948,20367690798,40850961478,78277647728,
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`%U 144113836976,256112415570,441063276882,738481048172,1205470385252
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`%N Number of 4 X 4 0..n arrays with row and column sums one greater than the previous row and column.
`

`%C Row 4 of A202864.
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`%F Empirical: a(n) = (2789/37800)*n^10 + (2789/3780)*n^9 + (6673/2520)*n^8 + (73/21)*n^7 - (1673/1800)*n^6 - (929/180)*n^5 - (14359/7560)*n^4 + (521/189)*n^3 + (3487/3150)*n^2 - (17/21)*n.
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`%e Some solutions for n=3
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`%e ..0..2..0..3....0..1..0..2....2..0..2..2....0..0..1..3....0..0..1..3
`

`%e ..0..2..1..3....0..1..0..3....0..3..1..3....0..2..3..0....1..2..1..1
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`%e ..2..0..3..2....1..1..3..0....2..1..3..2....1..0..2..3....2..0..2..2
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`%e ..3..2..3..0....2..1..2..1....2..3..2..2....3..3..0..1....1..3..2..1
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`%Y Cf. A202864.
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`%K nonn
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`%O 1,1
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`%A _R. H. Hardin_, Dec 25 2011
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