|
%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
| 