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A240626 Number of nX3 0..3 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..3 introduced in row major order.

%I A240626 #6 Jul 23 2025 11:02:48
%S A240626 4,109,4369,180480,7462748,308596193,12761076882,527696013254,
%T A240626 21821286982448,902353910690193,37314141073241635,1543014450929326860,
%U A240626 63806737265585893957,2638536352033321770102,109108761540671975977499
%N A240626 Number of nX3 0..3 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..3 introduced in row major order.
%C A240626 Column 3 of A240629
%H A240626 R. H. Hardin, <a href="/A240626/b240626.txt">Table of n, a(n) for n = 1..210</a>
%F A240626 Empirical: a(n) = 42*a(n-1) -20*a(n-2) -142*a(n-3) -5711*a(n-4) -3710*a(n-5) +80515*a(n-6) +372388*a(n-7) -2230154*a(n-8) +4624628*a(n-9) -9890649*a(n-10) +14198608*a(n-11) -3659227*a(n-12) -14748976*a(n-13) +83450532*a(n-14) -193948732*a(n-15) +312395335*a(n-16) -431237402*a(n-17) +231099273*a(n-18) +119705446*a(n-19) -536897174*a(n-20) +821278530*a(n-21) -566571559*a(n-22) +608221048*a(n-23) -508930511*a(n-24) +335483670*a(n-25) +83749796*a(n-26) -1224993018*a(n-27) +1081779799*a(n-28) -819999594*a(n-29) -208353027*a(n-30) +140757132*a(n-31) +622919226*a(n-32) +311776740*a(n-33) +25763409*a(n-34) +1679390712*a(n-35) -88064901*a(n-36) +41324256*a(n-37) +852316668*a(n-38) -80513676*a(n-39) -299431647*a(n-40) -419191038*a(n-41) -212845401*a(n-42) -113413446*a(n-43) -328430538*a(n-44) -226393866*a(n-45) -43046721*a(n-46)
%e A240626 Some solutions for n=4
%e A240626 ..0..1..1....0..1..2....0..1..2....0..0..1....0..1..0....0..0..1....0..1..1
%e A240626 ..0..2..3....0..1..2....0..2..1....1..2..2....1..2..3....2..1..1....0..2..0
%e A240626 ..3..3..1....1..3..1....1..3..0....2..0..1....2..0..3....3..0..1....3..2..0
%e A240626 ..0..1..0....1..0..2....1..2..2....1..2..3....1..1..0....0..1..0....3..0..3
%K A240626 nonn
%O A240626 1,1
%A A240626 _R. H. Hardin_, Apr 09 2014