A269109 T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three no more than once.

4, 16, 16, 60, 180, 60, 216, 1740, 1740, 216, 756, 15540, 40908, 15540, 756, 2592, 132300, 872460, 872460, 132300, 2592, 8748, 1090740, 17593092, 43964700, 17593092, 1090740, 8748, 29160, 8787660, 342055548, 2085484068, 2085484068

Offset

1,1

Comments

Table starts

......4.........16.............60................216....................756

.....16........180...........1740..............15540.................132300

.....60.......1740..........40908.............872460...............17593092

....216......15540.........872460...........43964700.............2085484068

....756.....132300.......17593092.........2085484068...........232068730044

...2592....1090740......342055548........95166487524.........24808345933548

...8748....8787660.....6482020140......4227147007836.......2579398703502996

..29160...69580980...120520189980....184069947098892.....262780733311913580

..96228..543538380..2208175854948...7894012975085748...26357371124964908460

.314928.4200069300.39988864047276.334480929126425748.2611360040338484328156

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

Formula

Empirical for column k:

k=1: a(n) = 6*a(n-1) -9*a(n-2)

k=2: a(n) = 14*a(n-1) -49*a(n-2) for n>3

k=3: a(n) = 36*a(n-1) -378*a(n-2) +972*a(n-3) -729*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=3 k=4
..0..0..1..2. .0..2..2..0. .0..1..1..1. .0..2..3..1. .2..0..1..0
..0..2..3..3. .0..2..0..1. .0..0..3..1. .0..0..1..3. .0..0..1..1
..1..3..1..3. .1..0..0..2. .0..2..2..3. .0..0..0..2. .2..2..2..3

Crossrefs

Column 1 is A120926(n+1).

Sequence in context: A207535 A269194 A269143 * A269201 A269289 A267933

Adjacent sequences: A269106 A269107 A269108 * A269110 A269111 A269112

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 19 2016

Status

approved