login
Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,0,1,1,1 for x=0,1,2,3,4
1

%I #5 Mar 31 2012 12:36:29

%S 1,16,53,275,780,5713,16773,98870,393913,1869033,8527840,32730687,

%T 177791439,674100600,3386483171,13856198755,66236228308,289604893615,

%U 1242844626331,5912414575588,24990706118619,116867053171491

%N Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,0,1,1,1 for x=0,1,2,3,4

%C Every 0 is next to 0 0's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 1's, every 4 is next to 4 1's

%C Column 4 of A197250

%H R. H. Hardin, <a href="/A197246/b197246.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-2) +12*a(n-3) +134*a(n-4) +160*a(n-5) -615*a(n-6) +12174*a(n-7) -518*a(n-8) -47245*a(n-9) -44364*a(n-10) +38534*a(n-11) +120522*a(n-12) -170702*a(n-13) -87919*a(n-14) -4472*a(n-15) +682511*a(n-16) -390368*a(n-17) +333704*a(n-18) -949248*a(n-19) +1346705*a(n-20) -1109007*a(n-21) +1033190*a(n-22) -2853866*a(n-23) +1697513*a(n-24) +872394*a(n-25) +1858574*a(n-26) +533223*a(n-27) -3166721*a(n-28) +1038785*a(n-29) -2246717*a(n-30) +2216266*a(n-31) -1520506*a(n-32) +1327738*a(n-33) -734503*a(n-34) +531200*a(n-35) -302942*a(n-36) +85056*a(n-37) -52786*a(n-38) +18048*a(n-39) +9507*a(n-40) -770*a(n-41) +911*a(n-42) -852*a(n-43) +25*a(n-44) +25*a(n-45) -180*a(n-46) -55*a(n-47) +15*a(n-48) +10*a(n-49) for n>50

%e Some solutions containing all values 0 to 4 for n=5

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

%e ..1..2..3..1....0..1..3..1....2..1..4..1....3..1..4..1....1..3..2..1

%e ..1..0..1..3....1..4..1..0....1..0..1..2....1..4..1..0....3..1..0..1

%e ..1..1..4..1....3..1..4..1....2..1..1..0....0..1..3..1....1..4..1..1

%e ..0..1..1..0....1..0..1..2....0..1..3..1....1..1..0..1....0..1..2..0

%K nonn

%O 1,2

%A _R. H. Hardin_ Oct 12 2011