login
T(n,k)=Number of (n+1)X(k+1) 0..5 arrays with every 2X2 subblock having the sum of the squares of the edge differences equal to 14 (14 maximizes T(1,1))
9

%I #4 Dec 14 2013 08:39:27

%S 144,772,772,3984,5232,3984,20936,36784,36784,20936,108864,272564,

%T 364512,272564,108864,570208,2012472,3945444,3945444,2012472,570208,

%U 2971200,15071680,42895672,64384744,42895672,15071680,2971200,15541312,112180004

%N T(n,k)=Number of (n+1)X(k+1) 0..5 arrays with every 2X2 subblock having the sum of the squares of the edge differences equal to 14 (14 maximizes T(1,1))

%C Table starts

%C .......144.........772..........3984............20936.............108864

%C .......772........5232.........36784...........272564............2012472

%C ......3984.......36784........364512..........3945444...........42895672

%C .....20936......272564.......3945444.........64384744.........1066468816

%C ....108864.....2012472......42895672.......1066468816........27145405344

%C ....570208....15071680.....478087900......18298607052.......724755509708

%C ...2971200...112180004....5291663768.....311919115144.....19199171263648

%C ..15541312...840367588...59202020744....5398974995872....519677244552168

%C ..81063040..6267926076..658067704512...92678590515300..13905091332351288

%C .423704496.46922305260.7360796797308.1605489993650956.377054658397332732

%H R. H. Hardin, <a href="/A233653/b233653.txt">Table of n, a(n) for n = 1..112</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 9]

%F k=2: [order 38]

%e Some solutions for n=2 k=4

%e ..3..2..3..3..4....0..3..5..4..5....0..3..0..3..4....2..3..3..0..1

%e ..3..0..0..1..4....0..2..2..2..5....0..2..2..3..1....0..0..1..0..3

%e ..3..2..3..3..3....0..3..0..3..3....3..3..5..3..4....1..3..3..0..1

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 14 2013