A234114 - OEIS

%I #4 Dec 19 2013 16:27:23

%S 56,186,186,604,608,604,2064,2086,2086,2064,6964,7742,7732,7742,6964,

%T 24156,29278,31740,31740,29278,24156,83012,113666,133592,151304,

%U 133592,113666,83012,290164,446590,581756,738628,738628,581756,446590,290164

%N T(n,k)=Number of (n+1)X(k+1) 0..4 arrays with every 2X2 subblock having the sum of the absolute values of all six edge and diagonal differences equal to 12

%C Table starts

%C ......56......186.......604.......2064........6964........24156.........83012

%C .....186......608......2086.......7742.......29278.......113666........446590

%C .....604.....2086......7732......31740......133592.......581756.......2579864

%C ....2064.....7742.....31740.....151304......738628......3840512......20547980

%C ....6964....29278....133592.....738628.....4093912.....24612244.....150134376

%C ...24156...113666....581756....3840512....24612244....178269116....1293718300

%C ...83012...446590...2579864...20547980...150134376...1293718300...10603143992

%C ..290164..1777146..11668144..114726620...965407560..10243412736...97572997380

%C .1007972..7128062..53568572..659505140..6359501076..83539101944..892457433308

%C .3540836.28800050.249460672.3907997608.43513496776.726030071196.8881590361884

%H R. H. Hardin, <a href="/A234114/b234114.txt">Table of n, a(n) for n = 1..144</a>

%F Empirical for column k:

%F k=1: a(n) = 5*a(n-1) +6*a(n-2) -50*a(n-3) +16*a(n-4) +80*a(n-5) -16*a(n-6)

%F k=2: [order 18]

%F k=3: [order 40]

%F k=4: [order 96]

%e Some solutions for n=4 k=4

%e ..3..3..4..3..4....3..3..3..0..3....1..0..1..1..4....0..4..0..4..4

%e ..4..0..3..0..3....4..0..0..3..4....4..1..4..0..1....1..1..1..1..1

%e ..0..0..3..0..3....3..3..3..0..3....1..4..1..1..4....0..4..0..4..0

%e ..0..4..3..4..3....0..4..0..3..0....0..1..4..0..1....0..0..0..0..0

%e ..3..3..0..3..0....4..4..4..3..4....1..4..1..1..4....3..3..3..3..3

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 19 2013