A231957 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every element equal to some horizontal, vertical, diagonal or antidiagonal neighbor, with top left element zero

4, 18, 18, 64, 142, 64, 236, 1034, 1034, 236, 888, 7756, 14842, 7756, 888, 3336, 58350, 220472, 220472, 58350, 3336, 12512, 438540, 3292876, 6517534, 3292876, 438540, 12512, 46928, 3295580, 49124582, 193955142, 193955142, 49124582, 3295580, 46928

Offset

1,1

Comments

Table starts

......4.........18............64..............236.................888

.....18........142..........1034.............7756...............58350

.....64.......1034.........14842...........220472.............3292876

....236.......7756........220472..........6517534...........193955142

....888......58350.......3292876........193955142.........11501370840

...3336.....438540......49124582.......5764579644........681107245458

..12512....3295580.....732691918.....171279257338......40322931224352

..46928...24766738...10928482748....5089308419738....2387295795105696

.176032..186126146..163005613290..151223178459482..141340282653200376

.660320.1398767358.2431334781688.4493424899719612.8368067905547685676

Links

R. H. Hardin, Table of n, a(n) for n = 1..287

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) -2*a(n-2) +4*a(n-3)

k=2: a(n) = 7*a(n-1) +2*a(n-2) +13*a(n-3) +8*a(n-4)

k=3: [order 12]

k=4: [order 26]

k=5: [order 50]

Example

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

Crossrefs

Sequence in context: A064220 A205105 A371414 * A275952 A081420 A039277

Adjacent sequences: A231954 A231955 A231956 * A231958 A231959 A231960

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 15 2013

Status

approved