A205938 - OEIS

%I #7 Dec 10 2015 02:06:51

%S 1776,11028,81864,620988,4601832,34647764,258956760,1942182832,

%T 14548134360,109048169588,816513313600,6119001144252,45844697097568,

%U 343491408375096,2573223557463040,19280035339388884,144450083231226680

%N Number of (n+1) X 3 0..3 arrays with no 2 X 2 subblock having the number of clockwise edge increases equal to the number of counterclockwise edge increases in its adjacent leftward or upward neighbors.

%C Column 2 of A205944.

%H R. H. Hardin, <a href="/A205938/b205938.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 20*a(n-2) +106*a(n-3) +1073*a(n-4) +1676*a(n-5) -3921*a(n-6) +2510*a(n-7) +10367*a(n-8) -39660*a(n-9) -93737*a(n-10) +67098*a(n-11) +1223861*a(n-12) -354734*a(n-13) -10343391*a(n-14) +12014472*a(n-15) +13924079*a(n-16) -59795244*a(n-17) +51740047*a(n-18) +57373456*a(n-19) -110979072*a(n-20) +74835622*a(n-21) -35991056*a(n-22) -22750738*a(n-23) +144074425*a(n-24) -153484616*a(n-25) +22971007*a(n-26) +78260016*a(n-27) -114414927*a(n-28) +63699940*a(n-29) +5571416*a(n-30) -148244590*a(n-31) +124206264*a(n-32) -55439888*a(n-33) -56510828*a(n-34) +78816744*a(n-35) -51200538*a(n-36) -18471918*a(n-37) +26953636*a(n-38) -21588268*a(n-39) -34226*a(n-40) +2404520*a(n-41) -4650695*a(n-42) -885160*a(n-43) -143680*a(n-44) -32966*a(n-45) -70777*a(n-46) -35254*a(n-47) +10119*a(n-48) +3744*a(n-49) -981*a(n-50) -4*a(n-51) for n>54.

%e Some solutions for n=4:

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 01 2012