Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #4 Feb 16 2016 13:47:08
%S 3,9,9,24,60,27,60,240,336,81,144,912,2016,1728,243,336,3312,11664,
%T 15552,8448,729,768,11664,63792,136080,114048,39936,2187,1728,40176,
%U 339480,1125360,1504656,808704,184320,6561,3840,136080,1770048,9093528,18852912
%N T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.
%C Table starts
%C .....3........9.........24...........60............144..............336
%C .....9.......60........240..........912...........3312............11664
%C ....27......336.......2016........11664..........63792...........339480
%C ....81.....1728......15552.......136080........1125360..........9093528
%C ...243.....8448.....114048......1504656.......18852912........231730344
%C ...729....39936.....808704.....16061328......305242992.......5712070032
%C ..2187...184320....5598720....167226768.....4823705520.....137497776840
%C ..6561...835584...38071296...1709114256....74858700528....3251386055664
%C .19683..3735552..255301632..17218688400..1145496747312...75828095546544
%C .59049.16515072.1693052928.171498136464.17332683832944.1748970953035272
%H R. H. Hardin, <a href="/A268971/b268971.txt">Table of n, a(n) for n = 1..287</a>
%F Empirical for column k:
%F k=1: a(n) = 3*a(n-1)
%F k=2: a(n) = 8*a(n-1) -16*a(n-2)
%F k=3: a(n) = 12*a(n-1) -36*a(n-2)
%F k=4: a(n) = 18*a(n-1) -81*a(n-2) for n>3
%F k=5: a(n) = 30*a(n-1) -261*a(n-2) +540*a(n-3) -324*a(n-4)
%F k=6: a(n) = 50*a(n-1) -805*a(n-2) +4662*a(n-3) -12150*a(n-4) +14580*a(n-5) -6561*a(n-6)
%F k=7: [order 8]
%F Empirical for row n:
%F n=1: a(n) = 4*a(n-1) -4*a(n-2)
%F n=2: a(n) = 6*a(n-1) -9*a(n-2) for n>4
%F n=3: a(n) = 10*a(n-1) -29*a(n-2) +20*a(n-3) -4*a(n-4) for n>6
%F n=4: [order 6] for n>12
%F n=5: [order 14] for n>18
%F n=6: [order 18] for n>26
%F n=7: [order 54] for n>60
%e Some solutions for n=4 k=4
%e ..1..0..0..1. .2..1..0..1. .2..1..2..1. .2..1..2..1. .1..2..1..2
%e ..1..2..2..2. .0..0..2..2. .0..1..2..1. .1..2..2..1. .1..0..0..0
%e ..2..2..2..2. .1..2..2..2. .2..1..0..0. .2..2..2..2. .1..0..1..2
%e ..2..2..1..2. .2..1..2..2. .1..0..0..1. .2..2..1..0. .1..2..2..1
%Y Column 1 is A000244.
%Y Row 1 is A084858.
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 16 2016