A233883 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having the sum of the squares of all six edge and diagonal differences equal to 11 (11 maximizes T(1,1))

24, 76, 76, 240, 300, 240, 760, 1224, 1224, 760, 2400, 5156, 6200, 5156, 2400, 7600, 22020, 33656, 33656, 22020, 7600, 24000, 95464, 178704, 251532, 178704, 95464, 24000, 76000, 415092, 1015656, 1768660, 1768660, 1015656, 415092, 76000, 240000

Offset

1,1

Comments

Table starts

.....24.......76........240.........760..........2400...........7600

.....76......300.......1224........5156.........22020..........95464

....240.....1224.......6200.......33656........178704........1015656

....760.....5156......33656......251532.......1768660.......14111768

...2400....22020.....178704.....1768660......15013864......160334028

...7600....95464....1015656....14111768.....160334028.....2431002508

..24000...415092....5566176...103547288....1417225464....28822097624

..76000..1819604...32573400...858513368...16134545712...467398305988

.240000..7964808..181919416..6440961128..147047775280..5678281493816

.760000.35055940.1082482200.54554580804.1750029730452.96535463946148

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

Formula

Empirical for column k:

k=1: a(n) = 10*a(n-2)

k=2: a(n) = 3*a(n-1) +19*a(n-2) -60*a(n-3) +8*a(n-4) +36*a(n-5) -12*a(n-6)

k=3: a(n) = 56*a(n-2) -819*a(n-4) +2791*a(n-6) -3096*a(n-8) +961*a(n-10) -84*a(n-12)

k=4: [order 29]

k=5: [order 52]

Example

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

Crossrefs

Sequence in context: A378065 A265424 A033572 * A291630 A195027 A325958

Adjacent sequences: A233880 A233881 A233882 * A233884 A233885 A233886

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 17 2013

Status

approved