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A205408 Number of (n+2) X 3 0..2 arrays with every 3 X 3 subblock having three equal elements in a row horizontally, vertically or nw-to-se diagonally exactly two ways, and new values 0..2 introduced in row major order.

%I A205408 #7 Sep 10 2023 20:59:43
%S A205408 468,3868,33322,236576,1820215,14452683,109757792,844627201,
%T A205408 6555663807,50395116296,388310279461,2998496455277,23106198583152,
%U A205408 178125506630869,1373888878002903,10592170949339668,81666691848271821,629737361145882421
%N A205408 Number of (n+2) X 3 0..2 arrays with every 3 X 3 subblock having three equal elements in a row horizontally, vertically or nw-to-se diagonally exactly two ways, and new values 0..2 introduced in row major order.
%C A205408 Column 1 of A205415.
%H A205408 R. H. Hardin, <a href="/A205408/b205408.txt">Table of n, a(n) for n = 1..210</a>
%F A205408 Empirical: a(n) = 3*a(n-1) +15*a(n-2) +210*a(n-3) -46*a(n-4) -1180*a(n-5) -8860*a(n-6) -9460*a(n-7) +35477*a(n-8) +165003*a(n-9) +271917*a(n-10) -292806*a(n-11) -1718502*a(n-12) -2698834*a(n-13) -1465296*a(n-14) +4872048*a(n-15) +13801984*a(n-16) +30802224*a(n-17) +54371712*a(n-18) +14213752*a(n-19) -115878688*a(n-20) -314261840*a(n-21) -579542448*a(n-22) -599435264*a(n-23) +450034176*a(n-24) +2993109568*a(n-25) +6140523968*a(n-26) +5188675584*a(n-27) -5040264704*a(n-28) -21090059008*a(n-29) -30058399232*a(n-30) -12075326464*a(n-31) +39301468160*a(n-32) +79235510272*a(n-33) +29768392704*a(n-34) -75591352320*a(n-35) -84606517248*a(n-36) +10132783104*a(n-37) +59464876032*a(n-38) +26931363840*a(n-39).
%e A205408 Some solutions for n=3
%e A205408 ..0..0..0....0..0..0....0..0..1....0..0..1....0..0..0....0..0..0....0..1..2
%e A205408 ..1..1..2....0..1..2....2..0..1....1..1..1....0..0..0....1..0..2....0..2..2
%e A205408 ..0..0..0....0..1..2....1..0..0....0..1..1....1..1..2....0..1..0....0..1..2
%e A205408 ..2..2..2....0..2..2....0..0..0....0..0..0....2..2..2....1..1..1....0..1..2
%e A205408 ..1..2..1....0..2..2....2..1..0....0..2..2....2..0..2....0..0..0....1..1..1
%Y A205408 Cf. A205415.
%K A205408 nonn
%O A205408 1,1
%A A205408 _R. H. Hardin_, Jan 26 2012