A205986 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

81, 423, 423, 2232, 1980, 2232, 11568, 8004, 8004, 11568, 60432, 33504, 27060, 33504, 60432, 315357, 140802, 103998, 103998, 140802, 315357, 1643538, 591336, 408411, 419088, 408411, 591336, 1643538, 8574615, 2482596, 1599096, 1814784, 1814784

Offset

1,1

Comments

Table starts

......81......423.....2232.....11568......60432......315357......1643538

.....423.....1980.....8004.....33504.....140802......591336......2482596

....2232.....8004....27060....103998.....408411.....1599096......6296976

...11568....33504...103998....419088....1814784.....7793856.....35107968

...60432...140802...408411...1814784....9653376....50843904....279003648

..315357...591336..1599096...7793856...50843904...338009472...2260666464

.1643538..2482596..6296976..35107968..279003648..2260666464..19410499584

.8574615.10425528.24685680.152423040.1502833632.15125213376.160992300384

Links

R. H. Hardin, Table of n, a(n) for n = 1..612

Formula

Empirical for column k:

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)

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

k=3: a(n) = 60*a(n-3) +8*a(n-5) for n>9

k=4: a(n) = 84*a(n-3) for n>9

k=5: a(n) = 156*a(n-3) for n>10

k=6: a(n) = 300*a(n-3) for n>11

k=7: a(n) = 588*a(n-3) for n>12

k=8: a(n) = 1164*a(n-3) for n>13

k=9: a(n) = 2316*a(n-3) for n>14

k=10: a(n) = 4620*a(n-3) for n>15

k=11: a(n) = 9228*a(n-3) for n>16

k=12: a(n) = 18444*a(n-3) for n>17

k=13: a(n) = 36876*a(n-3) for n>18

apparently: a(n) = (36*2^(k-3) +12)*a(n-3) for n>k+5 and k>3

Example

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

Crossrefs

Sequence in context: A236155 A253449 A236148 * A206668 A238180 A206414

Adjacent sequences: A205983 A205984 A205985 * A205987 A205988 A205989

Keyword

nonn,tabl

Author

R. H. Hardin Feb 02 2012

Status

approved