A269829 T(n,k)=Number of nXk 0..4 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling four exactly once.

0, 5, 5, 40, 216, 40, 240, 3096, 3096, 240, 1280, 39784, 103296, 39784, 1280, 6400, 462680, 3200604, 3200604, 462680, 6400, 30720, 5145736, 90748696, 240637408, 90748696, 5145736, 30720, 143360, 55265336, 2472983556, 16644595392

Offset

1,2

Comments

Table starts

......0..........5.............40................240...................1280

......5........216...........3096..............39784.................462680

.....40.......3096.........103296............3200604...............90748696

....240......39784........3200604..........240637408............16644595392

...1280.....462680.......90748696........16644595392..........2840332868960

...6400....5145736.....2472983556......1109236460528........467693538063508

..30720...55265336....65284613232.....71730749075588......74936429415811576

.143360..580002280..1686961414812...4544255355000752...11771832152564634464

.655360.5978552216.42866673833128.283289815771686692.1821445245786662249776

Links

R. H. Hardin, Table of n, a(n) for n = 1..144

Formula

Empirical for column k:

k=1: a(n) = 8*a(n-1) -16*a(n-2)

k=2: [order 6] for n>7

k=3: [order 18] for n>19

k=4: [order 48] for n>49

Example

Some solutions for n=3 k=4
..0..0..3..3. .0..0..2..3. .0..0..2..3. .0..0..0..2. .0..1..4..1
..1..0..2..3. .0..1..3..3. .0..0..2..3. .1..0..1..0. .0..0..1..1
..1..1..3..3. .1..2..4..2. .3..3..3..0. .4..2..1..2. .0..1..2..1

Crossrefs

Sequence in context: A271289 A271083 A271277 * A270058 A270156 A270164

Adjacent sequences: A269826 A269827 A269828 * A269830 A269831 A269832

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 05 2016

Status

approved