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A232149 T(n,k)=Number of nXk 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally, diagonally or antidiagonally 9

%I #4 Nov 19 2013 08:28:02

%S 1,3,1,7,23,1,15,191,145,1,33,1299,3669,887,1,73,9097,67725,67311,

%T 5487,1,161,65837,1345057,3409361,1270511,33957,1,355,474721,27888353,

%U 191897041,177194147,23931701,210039,1,783,3410799,572956549,11346946019

%N T(n,k)=Number of nXk 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally, diagonally or antidiagonally

%C Table starts

%C .1.......3..........7.............15................33....................73

%C .1......23........191...........1299..............9097.................65837

%C .1.....145.......3669..........67725...........1345057..............27888353

%C .1.....887......67311........3409361.........191897041...........11346946019

%C .1....5487....1270511......177194147.......28299613241.........4807617578085

%C .1...33957...23931701.....9181257593.....4162183572673......2029709037695893

%C .1..210039..450210003...475203378037...611509764410977....855821105743586179

%C .1.1299219.8472530835.24603676419865.89867078251266793.360977861939388247605

%H R. H. Hardin, <a href="/A232149/b232149.txt">Table of n, a(n) for n = 1..97</a>

%F Empirical for column k:

%F k=2: a(n) = 5*a(n-1) +6*a(n-2) +8*a(n-3) +3*a(n-4) -8*a(n-5) -5*a(n-6)

%F k=3: [order 9]

%F k=4: [order 32]

%F k=5: [order 81]

%F Empirical for row n:

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

%F n=2: a(n) = 6*a(n-1) +4*a(n-2) +25*a(n-3) +60*a(n-4) -24*a(n-5) -72*a(n-6)

%F n=3: [order 19]

%F n=4: [order 58]

%e Some solutions for n=3 k=4

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

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

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

%Y Row 1 is A193641

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Nov 19 2013

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Last modified February 23 11:05 EST 2024. Contains 370283 sequences. (Running on oeis4.)