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A270058
T(n,k)=Number of nXk 0..4 arrays with some element plus some horizontally or vertically adjacent neighbor totalling four exactly once.
8
0, 5, 5, 40, 240, 40, 240, 5400, 5400, 240, 1280, 99840, 385200, 99840, 1280, 6400, 1683240, 22911300, 22911300, 1683240, 6400, 30720, 26891280, 1248460920, 4410058320, 1248460920, 26891280, 30720, 143360, 414705720, 64599504300
OFFSET
1,2
COMMENTS
Table starts
......0...........5...............40...................240
......5.........240.............5400.................99840
.....40........5400...........385200..............22911300
....240.......99840.........22911300............4410058320
...1280.....1683240.......1248460920..........779206497960
...6400....26891280......64599504300.......130850370606120
..30720...414705720....3230189811360.....21244602958557060
.143360..6237722400..157641639369300...3367363526042121600
.655360.92095515720.7554828673749960.524230216822482202860
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 8*a(n-1) -16*a(n-2)
k=2: a(n) = 26*a(n-1) -169*a(n-2) for n>3
k=3: a(n) = 90*a(n-1) -2257*a(n-2) +10440*a(n-3) -13456*a(n-4) for n>5
k=4: [order 6] for n>7
k=5: [order 14] for n>15
k=6: [order 26] for n>27
k=7: [order 64] for n>65
EXAMPLE
Some solutions for n=2 k=4
..4..3..1..0. .2..1..0..2. .3..3..4..3. .0..3..1..2. .0..3..4..3
..3..3..0..0. .1..4..0..1. .2..1..2..4. .1..0..1..0. .0..4..2..3
CROSSREFS
Column 1 is A269822.
Sequence in context: A271083 A271277 A269829 * A270156 A270164 A270181
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 09 2016
STATUS
approved