|
%I #5 Mar 31 2012 12:37:09
%S 81,423,423,2232,1980,2232,11568,8004,8004,11568,60432,33504,27060,
%T 33504,60432,315357,140802,103998,103998,140802,315357,1643538,591336,
%U 408411,419088,408411,591336,1643538,8574615,2482596,1599096,1814784,1814784
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X3 or 3X2 subblock having exactly two clockwise edge increases
%C Table starts
%C ......81......423.....2232.....11568......60432......315357......1643538
%C .....423.....1980.....8004.....33504.....140802......591336......2482596
%C ....2232.....8004....27060....103998.....408411.....1599096......6296976
%C ...11568....33504...103998....419088....1814784.....7793856.....35107968
%C ...60432...140802...408411...1814784....9653376....50843904....279003648
%C ..315357...591336..1599096...7793856...50843904...338009472...2260666464
%C .1643538..2482596..6296976..35107968..279003648..2260666464..19410499584
%C .8574615.10425528.24685680.152423040.1502833632.15125213376.160992300384
%H R. H. Hardin, <a href="/A205986/b205986.txt">Table of n, a(n) for n = 1..612</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) +10*a(n-2) +35*a(n-3) +a(n-4) +3*a(n-5) +a(n-6) +2*a(n-7)
%F k=2: a(n) = a(n-1) +7*a(n-2) +26*a(n-3) +5*a(n-4) -12*a(n-6) -4*a(n-7) for n>9
%F k=3: a(n) = 60*a(n-3) +8*a(n-5) for n>9
%F k=4: a(n) = 84*a(n-3) for n>9
%F k=5: a(n) = 156*a(n-3) for n>10
%F k=6: a(n) = 300*a(n-3) for n>11
%F k=7: a(n) = 588*a(n-3) for n>12
%F k=8: a(n) = 1164*a(n-3) for n>13
%F k=9: a(n) = 2316*a(n-3) for n>14
%F k=10: a(n) = 4620*a(n-3) for n>15
%F k=11: a(n) = 9228*a(n-3) for n>16
%F k=12: a(n) = 18444*a(n-3) for n>17
%F k=13: a(n) = 36876*a(n-3) for n>18
%F apparently: a(n) = (36*2^(k-3) +12)*a(n-3) for n>k+5 and k>3
%e Some solutions for n=4 k=3
%e ..0..0..0..1....1..0..0..0....1..1..2..1....1..2..2..2....0..1..1..0
%e ..1..2..1..1....1..2..1..1....0..1..1..2....2..2..1..0....0..2..0..2
%e ..0..1..1..2....2..1..1..2....1..2..1..1....2..1..0..0....0..1..1..2
%e ..1..1..2..0....1..1..2..1....1..1..2..0....1..0..0..2....2..1..1..0
%e ..1..2..0..0....0..0..0..0....0..1..1..1....0..0..1..0....2..0..2..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Feb 02 2012
| 