A204861 - OEIS

%I #5 Mar 31 2012 12:37:03

%S 382,1648,7127,31034,136899,603605,2660367,11721609,51702644,

%T 227902203,1004799769,4430100363,19531105570,86110306240,379643708799,

%U 1673789364704,7379441106496,32534731009926,143440092995732

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

%C Column 2 of A204867

%H R. H. Hardin, <a href="/A204861/b204861.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +7*a(n-2) +21*a(n-3) +a(n-4) -74*a(n-5) -162*a(n-6) +138*a(n-7) -18*a(n-8) +1187*a(n-9) -2509*a(n-10) -1249*a(n-11) +375*a(n-12) -3916*a(n-13) +29438*a(n-14) -20835*a(n-15) +21040*a(n-16) -41934*a(n-17) -21760*a(n-18) +100360*a(n-19) -54423*a(n-20) +171105*a(n-21) -190049*a(n-22) -55439*a(n-23) -103559*a(n-24) +4935*a(n-25) +72883*a(n-26) -32323*a(n-27) +95561*a(n-28) -221835*a(n-29) +320810*a(n-30) -176564*a(n-31) +95261*a(n-32) +33740*a(n-33) -115048*a(n-34) +86489*a(n-35) -210476*a(n-36) +35609*a(n-37) -117190*a(n-38) +191186*a(n-39) +95961*a(n-40) -27689*a(n-41) +89312*a(n-42) -83490*a(n-43) +9205*a(n-44) +61964*a(n-45) -55123*a(n-46) +33185*a(n-47) -16169*a(n-48) -5814*a(n-49) +12737*a(n-50) -3837*a(n-51) -410*a(n-52) -140*a(n-53) -740*a(n-54) +184*a(n-55) +104*a(n-56) -24*a(n-57) for n>58

%e Some solutions for n=3

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Jan 20 2012