A251326 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock having one or two 1s

10, 28, 28, 78, 116, 78, 220, 474, 474, 220, 618, 1982, 2804, 1982, 618, 1740, 8218, 17216, 17216, 8218, 1740, 4894, 34288, 104058, 157312, 104058, 34288, 4894, 13772, 142600, 636404, 1405454, 1405454, 636404, 142600, 13772, 38746, 594236, 3866110

Offset

1,1

Comments

Table starts

.....10.......28........78.........220...........618............1740

.....28......116.......474........1982..........8218...........34288

.....78......474......2804.......17216........104058..........636404

....220.....1982.....17216......157312.......1405454........12770802

....618.....8218....104058.....1405454......18415674.......246926340

...1740....34288....636404....12770802.....246926340......4911447738

...4894...142600...3866110...114913804....3265612528.....96040080726

..13772...594236..23591052..1040818716...43595364706...1900083059348

..38746..2473510.143559096..9388632290..578517868594..37310824370952

.109020.10302766.875140808.84916233072.7707617770032.736337217038262

Links

R. H. Hardin, Table of n, a(n) for n = 1..420

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) +8*a(n-2) -13*a(n-3) -a(n-4) +2*a(n-5)

k=3: [order 10]

k=4: [order 19]

k=5: [order 36]

k=6: [order 71]

Example

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

Crossrefs

Sequence in context: A196356 A196359 A184686 * A363133 A022422 A113962

Adjacent sequences: A251323 A251324 A251325 * A251327 A251328 A251329

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 01 2014

Status

approved