A232403 - OEIS

%I #4 Nov 23 2013 13:10:39

%S 28,124,484,2788,13532,71888,370876,1936620,10086748,52577472,

%T 274075468,1428659044,7447465900,38822542800,202377611840,

%U 1054972011608,5499454349924,28668065663684,149443551918676,779033262821720

%N Number of (n+1)X(5+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally or vertically, with no adjacent elements equal

%C Column 5 of A232406

%H R. H. Hardin, <a href="/A232403/b232403.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) +17*a(n-2) +a(n-3) -123*a(n-4) -246*a(n-5) +117*a(n-6) +1412*a(n-7) +2360*a(n-8) -1193*a(n-9) -11619*a(n-10) -15225*a(n-11) +14827*a(n-12) +64719*a(n-13) +47086*a(n-14) -94989*a(n-15) -216619*a(n-16) -56228*a(n-17) +315232*a(n-18) +434436*a(n-19) -23128*a(n-20) -587445*a(n-21) -525616*a(n-22) +114683*a(n-23) +585048*a(n-24) +411465*a(n-25) -56835*a(n-26) -288031*a(n-27) -202342*a(n-28) -30237*a(n-29) +41019*a(n-30) +28015*a(n-31) -5913*a(n-32) -9403*a(n-33) +42968*a(n-34) +67174*a(n-35) +33074*a(n-36) -48809*a(n-37) -68179*a(n-38) -16698*a(n-39) +34471*a(n-40) +28007*a(n-41) +85*a(n-42) -12424*a(n-43) -2982*a(n-44) +975*a(n-45) +1094*a(n-46) -263*a(n-47) -6*a(n-48) -7*a(n-49) -17*a(n-50) -7*a(n-51) +24*a(n-52) +22*a(n-53) +10*a(n-54) -4*a(n-55) -2*a(n-56)

%e Some solutions for n=4

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 23 2013