A270058 T(n,k)=Number of nXk 0..4 arrays with some element plus some horizontally or vertically adjacent neighbor totalling four exactly once.

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

R. H. Hardin, Table of n, a(n) for n = 1..180

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

Adjacent sequences: A270055 A270056 A270057 * A270059 A270060 A270061

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 09 2016

Status

approved