|
%I #4 Mar 08 2013 19:13:20
%S 1,2,2,3,7,3,7,34,34,7,20,389,991,389,20,67,7145,84521,84521,7145,67,
%T 255,179465,11047723,46407465,11047723,179465,255,1080,5426201,
%U 1639681049,30122054696,30122054696,1639681049,5426201,1080,5016,180390761
%N T(n,k)=Number of nXk 0..7 arrays with no element equal to another at a city block distance of exactly two, and new values 0..7 introduced in row major order
%C Table starts
%C ....1.........2............3..............7.............20.............67
%C ....2.........7...........34............389...........7145.........179465
%C ....3........34..........991..........84521.......11047723.....1639681049
%C ....7.......389........84521.......46407465....30122054696.20029573364121
%C ...20......7145.....11047723....30122054696.86240147780852
%C ...67....179465...1639681049.20029573364121
%C ..255...5426201.251412693667
%C .1080.180390761
%C .5016
%H R. H. Hardin, <a href="/A222894/b222894.txt">Table of n, a(n) for n = 1..49</a>
%F Empirical for column k:
%F k=1: a(n) = 22*a(n-1) -190*a(n-2) +820*a(n-3) -1849*a(n-4) +2038*a(n-5) -840*a(n-6) for n>8
%F k=2: a(n) = 66*a(n-1) -1353*a(n-2) +10648*a(n-3) -30096*a(n-4) +20736*a(n-5) for n>7
%F k=3: a(n) = 211*a(n-1) -9385*a(n-2) +110913*a(n-3) -253890*a(n-4) for n>6
%e Some solutions for n=3 k=4
%e ..0..1..2..2....0..1..2..3....0..1..2..3....0..1..2..3....0..1..1..2
%e ..3..4..5..3....2..4..4..5....4..1..5..6....4..5..5..1....2..3..4..4
%e ..5..2..1..4....6..0..0..2....2..3..0..6....6..3..4..0....5..5..6..7
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_ Mar 08 2013
| 