A206653 - OEIS

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

%S 390,1769,8374,39928,190577,910169,4345011,20745372,99072051,

%T 473072354,2258928115,10786845653,51508637025,245959541842,

%U 1174491287887,5608355555142,26780628595266,127881076950311,610649258608125

%N Number of (n+2)X4 0..1 arrays with every 3X3 subblock having three equal elements in a row horizontally, vertically or nw-to-se diagonally exactly two ways, and new values 0..1 introduced in row major order

%C Column 2 of A206659

%H R. H. Hardin, <a href="/A206653/b206653.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-2) +70*a(n-3) +111*a(n-4) +11*a(n-5) -1038*a(n-6) -2212*a(n-7) -1228*a(n-8) +6222*a(n-9) +14947*a(n-10) +4864*a(n-11) -21444*a(n-12) -37809*a(n-13) +37708*a(n-14) +69192*a(n-15) -16620*a(n-16) -247948*a(n-17) -181648*a(n-18) +265738*a(n-19) +294365*a(n-20) -25710*a(n-21) -311918*a(n-22) +1014729*a(n-23) +1556509*a(n-24) -3780019*a(n-25) -6949650*a(n-26) -2669749*a(n-27) +16905404*a(n-28) +19548332*a(n-29) -4383804*a(n-30) -36037146*a(n-31) -30507685*a(n-32) +15475748*a(n-33) +43855826*a(n-34) +30266708*a(n-35) -13081195*a(n-36) -21467990*a(n-37) -16915949*a(n-38) +7498639*a(n-39) +2382846*a(n-40) -6646771*a(n-41) +22164150*a(n-42) -20152361*a(n-43) -372616*a(n-44) -19073865*a(n-45) +18150630*a(n-46) +4473011*a(n-47) -14909593*a(n-48) +1916272*a(n-49) -15127805*a(n-50) +20327817*a(n-51) +1517558*a(n-52) -6955067*a(n-53) -6298662*a(n-54) +7138737*a(n-55) +6828905*a(n-56) -5259661*a(n-57) +1095788*a(n-58) +569873*a(n-59) +859792*a(n-60) +1148261*a(n-61) +401017*a(n-62) +1545245*a(n-63) +1189595*a(n-64) +590643*a(n-65) -31467*a(n-66) -26637*a(n-67) +275467*a(n-68) +196219*a(n-69) +198819*a(n-70) +39906*a(n-71) -32890*a(n-72) +32129*a(n-73) +8601*a(n-74) -1306*a(n-75) +613*a(n-76) -1805*a(n-77) -174*a(n-78) -1197*a(n-79) +21*a(n-80) +378*a(n-81) -27*a(n-82) for n>85

%e Some solutions for n=4

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Feb 11 2012