A295275 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 1 or 4 1s.

2, 4, 4, 7, 11, 7, 13, 33, 33, 13, 24, 98, 164, 98, 24, 44, 291, 811, 811, 291, 44, 81, 865, 4035, 6659, 4035, 865, 81, 149, 2570, 19997, 54773, 54773, 19997, 2570, 149, 274, 7637, 99245, 449827, 748740, 449827, 99245, 7637, 274, 504, 22693, 492401, 3697742

Offset

1,1

Comments

Table starts

...2.....4.......7........13..........24............44..............81

...4....11......33........98.........291...........865............2570

...7....33.....164.......811........4035.........19997...........99245

..13....98.....811......6659.......54773........449827.........3697742

..24...291....4035.....54773......748740......10203847.......139221499

..44...865...19997....449827....10203847.....230659662......5221177246

..81..2570...99245...3697742...139221499....5221177246....196091375073

.149..7637..492401..30386185..1898916677..118139247475...7361533108317

.274.22693.2443097.249719021.25902054180.2673342943199.276386201580189

Links

R. H. Hardin, Table of n, a(n) for n = 1..419

Formula

Empirical for column k:

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

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

k=3: [order 10]

k=4: [order 16]

k=5: [order 40]

k=6: [order 78]

Example

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

Crossrefs

Columns are A000073(n+3), A282990, A295270, A295271, A295272, A295273, A295274.

Diagonal is A295269.

Sequence in context: A296578 A268750 A282996 * A295253 A295652 A269075

Adjacent sequences: A295272 A295273 A295274 * A295276 A295277 A295278

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 19 2017

Status

approved