A232908 - OEIS

%I #4 Dec 02 2013 13:38:16

%S 0,10,4,52,34,8,82,320,194,12,432,2958,4928,1034,32,2372,27692,68310,

%T 62276,4986,84,8456,250934,1825972,1827866,761860,24498,184,29970,

%U 2338508,39641548,115154048,49501666,9880580,122994,412,132972,21159320

%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally or antidiagonally

%C Table starts

%C ....0.......10...........52..............82.................432

%C ....4.......34..........320............2958...............27692

%C ....8......194.........4928...........68310.............1825972

%C ...12.....1034........62276.........1827866...........115154048

%C ...32.....4986.......761860........49501666..........7517844304

%C ...84....24498......9880580......1295371950........485354122160

%C ..184...122994....123587140.....34359557398......31320663237216

%C ..412...613658...1571314692....911287659098....2024849938767040

%C ..976..3048362..19864803028..24111990771426..130826030730696144

%C .2276.15169602.251467184100.638690599346926.8452502440791870368

%H R. H. Hardin, <a href="/A232908/b232908.txt">Table of n, a(n) for n = 1..127</a>

%F Empirical for column k:

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

%F k=2: a(n) = 4*a(n-1) -a(n-2) +26*a(n-3) +16*a(n-4)

%F k=3: [order 8]

%F k=4: [order 18]

%F k=5: [order 34] for n>35

%F k=6: [order 75] for n>77

%F Empirical for row n:

%F n=1: a(n) = 4*a(n-2) +28*a(n-3) +80*a(n-4) +48*a(n-5) -67*a(n-6) -228*a(n-7) -224*a(n-8)

%F n=2: [order 29] for n>30

%e Some solutions for n=3 k=4

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

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

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

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

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Dec 02 2013