A206063 - OEIS

%I #5 Mar 31 2012 12:37:09

%S 256,2184,2184,19832,21140,19832,170688,167960,167960,170688,1499080,

%T 1390488,1278672,1390488,1499080,13136860,11638960,11155584,11155584,

%U 11638960,13136860,114770680,96831504,101369476,111242648,101369476

%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X3 or 3X2 subblock having exactly two clockwise edge increases

%C Table starts

%C ........256.......2184.......19832........170688........1499080

%C .......2184......21140......167960.......1390488.......11638960

%C ......19832.....167960.....1278672......11155584......101369476

%C .....170688....1390488....11155584.....111242648.....1198231144

%C ....1499080...11638960...101369476....1198231144....18209383140

%C ...13136860...96831504...910785080...12877680064...265284773176

%C ..114770680..805817696..8150091296..144759802024..4049733446192

%C .1005245456.6714115792.73102971728.1569116858248.62573461436920

%H R. H. Hardin, <a href="/A206063/b206063.txt">Table of n, a(n) for n = 1..263</a>

%F Empirical for column k:

%F k=1: a(n) = 3*a(n-1) +34*a(n-2) +145*a(n-3) -18*a(n-4) -2*a(n-5) +11*a(n-6) +6*a(n-7) +2*a(n-8) +4*a(n-9) for n>10

%F k=2: a(n) = 3*a(n-1) +20*a(n-2) +189*a(n-3) +102*a(n-4) +187*a(n-5) -612*a(n-6) -110*a(n-7) +186*a(n-8) +82*a(n-9) +43*a(n-10) -5*a(n-11) -16*a(n-12) for n>17

%F k=3: a(n) = a(n-2) +695*a(n-3) +2*a(n-4) +1693*a(n-5) -1278*a(n-7) +682*a(n-9) +286*a(n-11) +32*a(n-13) for n>20

%F k=4: a(n) = 1307*a(n-3) +24*a(n-4) +677*a(n-5) +44*a(n-6) +256*a(n-7) for n>16

%F k=5: a(n) = 3457*a(n-3) +526*a(n-5) for n>14

%F k=6: a(n) = 9491*a(n-3) +213*a(n-5) for n>15

%F k=7: a(n) = 26761*a(n-3) +573*a(n-5) for n>16

%e Some solutions for n=4 k=3

%e ..1..3..2..3....1..1..1..1....1..2..2..3....3..0..1..1....1..0..1..3

%e ..2..0..1..1....1..3..2..0....3..3..0..1....3..1..1..3....1..0..0..1

%e ..3..3..1..1....0..0..1..3....3..3..1..1....1..1..2..0....2..1..0..0

%e ..0..3..3..2....0..0..2..3....2..1..1..0....2..3..3..0....2..0..3..3

%e ..2..0..3..0....2..1..1..1....3..1..2..1....0..3..3..1....2..1..3..0

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Feb 03 2012