A205051 - OEIS

%I #5 Mar 31 2012 12:37:04

%S 2892,19151,182720,1887956,24394205,274053256,3582717434,40560306665,

%T 528619776909,6007525824270,78011222099753,889719151865578,

%U 11513567328881604,131755174926725810,1699414929821586134

%N Number of (n+1)X5 0..2 arrays with the number of rightwards and downwards edge increases in each 2X2 subblock equal to the number in all its horizontal and vertical neighbors

%C Column 4 of A205055

%H R. H. Hardin, <a href="/A205051/b205051.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 11*a(n-1) +89*a(n-2) -1382*a(n-3) +7232*a(n-4) -20487*a(n-5) +22608*a(n-6) +90684*a(n-7) -610247*a(n-8) +1980976*a(n-9) -4332786*a(n-10) +6534588*a(n-11) -5158482*a(n-12) -7408327*a(n-13) +52395654*a(n-14) -198568574*a(n-15) +640307615*a(n-16) -1784288800*a(n-17) +4149738810*a(n-18) -7865157646*a(n-19) +12022512128*a(n-20) -14747342533*a(n-21) +14833163265*a(n-22) -14571366419*a(n-23) +20348606706*a(n-24) -37020899614*a(n-25) +60754513871*a(n-26) -81818119908*a(n-27) +95454358474*a(n-28) -104095887630*a(n-29) +108382444060*a(n-30) -104058755817*a(n-31) +89676294881*a(n-32) -70419789643*a(n-33) +52267259062*a(n-34) -37130931142*a(n-35) +24661764862*a(n-36) -14989718717*a(n-37) +8451156047*a(n-38) -4594292260*a(n-39) +2445305996*a(n-40) -1225764216*a(n-41) +547225764*a(n-42) -215269088*a(n-43) +80229956*a(n-44) -30902380*a(n-45) +11440836*a(n-46) -3344076*a(n-47) +633600*a(n-48) -57600*a(n-49) for n>54

%e Some solutions for n=4

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Jan 21 2012