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 A233073 T(n,k)=Number of nXk 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 in row major order 7

%I #4 Dec 03 2013 20:48:05

%S 1,2,2,5,9,5,14,50,50,14,41,289,582,289,41,122,1682,6854,6854,1682,

%T 122,365,9801,80811,164495,80811,9801,365,1094,57122,952869,3957778,

%U 3957778,952869,57122,1094,3281,332929,11235652,95264272,194998895,95264272

%N T(n,k)=Number of nXk 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 in row major order

%C Table starts

%C ....1........2...........5.............14................41

%C ....2........9..........50............289..............1682

%C ....5.......50.........582...........6854.............80811

%C ...14......289........6854.........164495...........3957778

%C ...41.....1682.......80811........3957778.........194998895

%C ..122.....9801......952869.......95264272........9622519979

%C ..365....57122....11235652.....2293174089......475027244071

%C .1094...332929...132484030....55201144642....23452561697310

%C .3281..1940450..1562171807..1328800293991..1157902539075279

%C .9842.11309769.18420188169.31986846738550.57168401542703366

%H R. H. Hardin, <a href="/A233073/b233073.txt">Table of n, a(n) for n = 1..264</a>

%F Empirical for column k:

%F k=1: a(n) = 4*a(n-1) -3*a(n-2)

%F k=2: a(n) = 7*a(n-1) -7*a(n-2) +a(n-3)

%F k=3: a(n) = 14*a(n-1) -28*a(n-2) +24*a(n-3) -11*a(n-4) +2*a(n-5) for n>6

%F k=4: [order 11] for n>12

%F k=5: [order 21] for n>23

%F k=6: [order 58] for n>60

%e Some solutions for n=4 k=4

%e ..0..0..1..0....0..0..1..1....0..0..0..0....0..1..0..1....0..0..1..1

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

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

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

%Y Column 1 is A007051(n-1)

%Y Column 2 is A115599

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Dec 03 2013

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Last modified July 13 18:16 EDT 2024. Contains 374285 sequences. (Running on oeis4.)