A233883 - OEIS

%I #4 Dec 17 2013 07:11:14

%S 24,76,76,240,300,240,760,1224,1224,760,2400,5156,6200,5156,2400,7600,

%T 22020,33656,33656,22020,7600,24000,95464,178704,251532,178704,95464,

%U 24000,76000,415092,1015656,1768660,1768660,1015656,415092,76000,240000

%N 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))

%C Table starts

%C .....24.......76........240.........760..........2400...........7600

%C .....76......300.......1224........5156.........22020..........95464

%C ....240.....1224.......6200.......33656........178704........1015656

%C ....760.....5156......33656......251532.......1768660.......14111768

%C ...2400....22020.....178704.....1768660......15013864......160334028

%C ...7600....95464....1015656....14111768.....160334028.....2431002508

%C ..24000...415092....5566176...103547288....1417225464....28822097624

%C ..76000..1819604...32573400...858513368...16134545712...467398305988

%C .240000..7964808..181919416..6440961128..147047775280..5678281493816

%C .760000.35055940.1082482200.54554580804.1750029730452.96535463946148

%H R. H. Hardin, <a href="/A233883/b233883.txt">Table of n, a(n) for n = 1..264</a>

%F Empirical for column k:

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

%F 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)

%F 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)

%F k=4: [order 29]

%F k=5: [order 52]

%e Some solutions for n=3 k=4

%e ..0..1..2..1..0....1..2..1..2..1....0..2..2..0..0....1..0..1..2..1

%e ..2..0..0..2..0....2..0..0..2..0....1..0..1..2..1....2..2..0..0..2

%e ..0..1..2..1..2....0..1..2..1..2....2..2..0..2..0....1..0..1..2..1

%e ..2..0..0..0..2....0..2..0..2..0....0..1..0..1..0....2..0..2..0..0

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 17 2013