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Number of nX3 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of elements above it, modulo 4
1

%I #4 Mar 23 2014 06:59:37

%S 8,92,1182,13476,158728,1864886,21813374,255830770,2997975560,

%T 35134044112,411772022880,4825831891850,56557172387854,

%U 662835950459020,7768238700938098,91041566963856564,1066981238248658526

%N Number of nX3 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of elements above it, modulo 4

%C Column 3 of A239649

%H R. H. Hardin, <a href="/A239644/b239644.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +103*a(n-2) +305*a(n-3) -1576*a(n-4) -7517*a(n-5) +13822*a(n-6) +84263*a(n-7) -193487*a(n-8) -386588*a(n-9) +2125542*a(n-10) -2240531*a(n-11) -6903934*a(n-12) +24598571*a(n-13) -24037070*a(n-14) -20933507*a(n-15) +84761410*a(n-16) -76409880*a(n-17) -58972949*a(n-18) +191904430*a(n-19) -103074732*a(n-20) -119505780*a(n-21) +301528072*a(n-22) -71474328*a(n-23) -220257104*a(n-24) +158665984*a(n-25) -141276800*a(n-26) -317537024*a(n-27) -19131392*a(n-28) -71272448*a(n-29) -128999424*a(n-30) -20832256*a(n-31) -5177344*a(n-32) -4849664*a(n-33) +1048576*a(n-34) +524288*a(n-35)

%e Some solutions for n=5

%e ..1..0..3....3..0..1....1..3..1....1..3..3....3..0..1....1..0..0....3..0..0

%e ..1..0..0....3..1..1....2..0..0....2..0..0....2..0..1....2..0..3....2..0..1

%e ..2..1..0....1..0..3....2..3..2....2..3..3....1..3..2....2..3..0....1..0..2

%e ..1..0..2....3..1..2....2..1..2....1..2..1....2..3..3....1..3..3....2..1..0

%e ..2..0..0....1..3..3....3..2..0....2..3..3....1..3..2....1..3..2....1..2..0

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 23 2014