A268809 T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

3, 9, 9, 24, 34, 24, 60, 104, 104, 60, 144, 290, 332, 290, 144, 336, 772, 1202, 1202, 772, 336, 768, 1972, 4158, 5848, 4158, 1972, 768, 1728, 4914, 14308, 28452, 28452, 14308, 4914, 1728, 3840, 12010, 48460, 135912, 195384, 135912, 48460, 12010, 3840, 8448

Offset

1,1

Comments

Table starts

....3.....9......24.......60........144.........336...........768

....9....34.....104......290........772........1972..........4914

...24...104.....332.....1202.......4158.......14308.........48460

...60...290....1202.....5848......28452......135912........640926

..144...772....4158....28452.....195384.....1316226.......8734264

..336..1972...14308...135912....1316226....12432856.....115671422

..768..4914...48460...640926....8734264...115671422....1508087180

.1728.12010..162722..2990786...57302798..1062318610...19390335102

.3840.28922..541744.13835892..372342650..9657289546..246666802206

.8448.68836.1791504.63544542.2400532536.87052567448.3110082281974

Links

R. H. Hardin, Table of n, a(n) for n = 1..637

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) -4*a(n-2)

k=2: a(n) = 2*a(n-1) +3*a(n-2) -2*a(n-3) -6*a(n-4) -4*a(n-5) -a(n-6) for n>7

k=3: [order 10] for n>12

k=4: [order 16] for n>19

k=5: [order 26] for n>29

k=6: [order 42] for n>45

k=7: [order 68] for n>71

Example

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

Crossrefs

Column 1 is A084858.

Sequence in context: A207235 A207228 A207015 * A268628 A269052 A268971

Adjacent sequences: A268806 A268807 A268808 * A268810 A268811 A268812

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 13 2016

Status

approved