%I #4 Nov 23 2013 07:58:16
%S 18,64,192,840,3246,12818,51240,203104,809436,3222418,12842530,
%T 51200418,204173560,814433476,3249025434,12962845362,51721055986,
%U 206371682824,823458800224,3285784448274,13111130921510,52317080184316
%N Number of (n+1)X(2+1) 0..3 arrays with every element next to itself plus and minus one within the range 0..3 horizontally, vertically or antidiagonally, with no adjacent elements equal
%C Column 2 of A232391
%H R. H. Hardin, <a href="/A232385/b232385.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 8*a(n-1) -12*a(n-2) -46*a(n-3) +114*a(n-4) +144*a(n-5) -515*a(n-6) -92*a(n-7) +1013*a(n-8) -174*a(n-9) -1106*a(n-10) -180*a(n-11) +1863*a(n-12) +1362*a(n-13) -1357*a(n-14) -4530*a(n-15) -4185*a(n-16) +2834*a(n-17) +10896*a(n-18) +23586*a(n-19) +20961*a(n-20) -27828*a(n-21) -85764*a(n-22) -67736*a(n-23) +16447*a(n-24) +51480*a(n-25) +18353*a(n-26) +24172*a(n-27) +46154*a(n-28) -23844*a(n-29) -138921*a(n-30) -121870*a(n-31) +20563*a(n-32) +112782*a(n-33) +73329*a(n-34) -13992*a(n-35) -47929*a(n-36) -26326*a(n-37) -1725*a(n-38) +4784*a(n-39) +2921*a(n-40) +938*a(n-41) +190*a(n-42) +16*a(n-43) -a(n-44)
%e Some solutions for n=7
%e ..2..1..0....3..0..2....1..0..3....2..3..1....3..1..2....0..1..2....3..2..3
%e ..3..2..3....2..1..3....2..1..2....1..0..2....2..0..3....2..0..3....1..0..2
%e ..1..0..1....3..0..1....3..0..3....2..1..3....3..1..2....3..1..2....3..1..0
%e ..2..3..2....1..3..2....2..1..0....3..0..2....0..3..1....2..3..0....2..3..2
%e ..1..0..1....2..0..3....0..2..3....2..1..0....1..2..0....1..2..1....0..1..3
%e ..3..2..3....3..1..2....1..0..1....0..2..1....0..3..2....0..3..2....3..0..2
%e ..1..0..1....2..0..1....2..3..2....1..3..2....1..0..1....2..0..1....2..1..0
%e ..2..3..2....3..2..0....1..0..3....2..0..1....2..3..0....1..2..3....3..2..3
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 23 2013
|