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A204680 Number of nX3 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..3 introduced in row major order.

%I A204680 #8 Jul 22 2025 18:13:19
%S A204680 4,159,6451,287379,12711292,563046972,24932875448,1104148318540,
%T A204680 48896363697435,2165344586789384,95890854634053213,
%U A204680 4246463765107286355,188051863862618823831,8327753561924846574597,368789108809170527549222
%N A204680 Number of nX3 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..3 introduced in row major order.
%C A204680 Column 3 of A204685
%H A204680 R. H. Hardin, <a href="/A204680/b204680.txt">Table of n, a(n) for n = 1..210</a>
%F A204680 Empirical: a(n) = 33*a(n-1) +576*a(n-2) -2576*a(n-3) -38824*a(n-4) +127580*a(n-5) +909748*a(n-6) -3116838*a(n-7) -7687952*a(n-8) +37104276*a(n-9) -63026296*a(n-10) -432695012*a(n-11) +2720629849*a(n-12) -5107909211*a(n-13) +3025539132*a(n-14) +16236494388*a(n-15) -61214998652*a(n-16) +60381991332*a(n-17) +26465066916*a(n-18) -101087636628*a(n-19) +92416374336*a(n-20) +14995740528*a(n-21) -85493406672*a(n-22) +58756380048*a(n-23) +4342368528*a(n-24) -38953846080*a(n-25) +13150955232*a(n-26) +1077909120*a(n-27) -6291032832*a(n-28) +3193509888*a(n-29) +1854296064*a(n-30) for n>33
%e A204680 Some solutions for n=5
%e A204680 ..0..1..1....0..0..1....0..0..1....0..0..1....0..0..1....0..0..1....0..0..1
%e A204680 ..0..0..1....2..1..2....0..1..0....0..0..1....0..0..1....2..3..1....2..2..1
%e A204680 ..2..0..2....2..3..0....2..3..3....1..2..2....1..2..2....1..1..3....0..3..2
%e A204680 ..2..1..1....1..3..2....0..1..0....3..2..2....0..1..3....3..3..1....2..0..2
%e A204680 ..3..1..0....1..1..2....1..2..1....3..3..1....1..3..3....0..1..1....3..3..1
%K A204680 nonn
%O A204680 1,1
%A A204680 _R. H. Hardin_ Jan 18 2012