A205636 - OEIS

%I #7 Oct 09 2015 04:28:14

%S 2320,28724,377568,5079336,69574220,962953968,13444055224,

%T 188823193784,2664428266336,37723583696052,535447018219820,

%U 7614062720813020,108418400331562368,1545312836738950012,22041527502028941280

%N Number of (n+1)X3 0..3 arrays with every 2 X 2 subblock having the number of clockwise edge increases equal to the number of counterclockwise edge increases in its adjacent leftward and upward neighbors.

%C Column 2 of A205642.

%H R. H. Hardin, <a href="/A205636/b205636.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 40*a(n-1) -538*a(n-2) +1600*a(n-3) +26601*a(n-4) -244741*a(n-5) +233209*a(n-6) +5541744*a(n-7) -21842748*a(n-8) -32944767*a(n-9) +354353234*a(n-10) -303682333*a(n-11) -2646718872*a(n-12) +5934353280*a(n-13) +9289012973*a(n-14) -41577894950*a(n-15) -1914076326*a(n-16) +162268698987*a(n-17) -118745894358*a(n-18) -375952312601*a(n-19) +516190082301*a(n-20) +490860223665*a(n-21) -1126227747881*a(n-22) -278402542035*a(n-23) +1492073391103*a(n-24) -58128143145*a(n-25) -1376232661944*a(n-26) +209754887441*a(n-27) +989829393787*a(n-28) -250378408153*a(n-29) -438696247203*a(n-30) +73070040366*a(n-31) +159024306012*a(n-32) +15073020296*a(n-33) -63596130670*a(n-34) -2882562568*a(n-35) +13670636368*a(n-36) -797920044*a(n-37) -999511826*a(n-38) +247638480*a(n-39) -138158645*a(n-40) +29008218*a(n-41) +1133604*a(n-42) -336960*a(n-43) for n>45.

%e Some solutions for n=4:

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 29 2012