A233644 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having the sum of the squares of the edge differences equal to 2 (2 maximizes T(1,1))

24, 90, 90, 324, 534, 324, 1188, 3004, 3004, 1188, 4320, 17424, 26192, 17424, 4320, 15768, 99380, 238570, 238570, 99380, 15768, 57456, 572192, 2118568, 3455622, 2118568, 572192, 57456, 209520, 3277236, 19123682, 48384788, 48384788, 19123682

Offset

1,1

Comments

Table starts

......24........90..........324...........1188.............4320

......90.......534.........3004..........17424............99380

.....324......3004........26192.........238570..........2118568

....1188.....17424.......238570........3455622.........48384788

....4320.....99380......2118568.......48384788.......1060656512

...15768....572192.....19123682......694104494......24003655980

...57456...3277236....170872144.....9797170648.....531400908604

..209520..18825580...1536664586...139850230232...11957878063196

..763776.107963840..13763062452..1981047775126..265950544067684

.2784672.619734876.123586823454.28211321138046.5965795563741028

Links

R. H. Hardin, Table of n, a(n) for n = 1..312

Formula

Empirical for column k:

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

k=2: a(n) = 6*a(n-1) +9*a(n-2) -67*a(n-3) +26*a(n-4) +81*a(n-5) -48*a(n-6) +2*a(n-7)

k=3: [order 13]

k=4: [order 31]

k=5: [order 66]

Example

Some solutions for n=3 k=4
..0..0..0..1..1....2..1..2..2..2....1..0..1..0..0....1..1..1..1..1
..0..1..1..1..0....1..1..1..1..1....1..0..1..0..1....0..0..1..2..1
..1..1..0..1..0....0..0..0..0..0....0..0..1..1..1....1..1..1..1..1
..0..1..0..1..0....0..1..1..0..1....1..0..0..1..2....1..2..2..2..1

Crossrefs

Sequence in context: A044592 A211632 A305888 * A010012 A256718 A233637

Adjacent sequences: A233641 A233642 A233643 * A233645 A233646 A233647

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 14 2013

Status

approved