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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 one plus the sum of elements above it, modulo 4
1

%I #4 Mar 27 2014 09:05:56

%S 10,132,1480,17552,204779,2405330,28156167,330152684,3868656623,

%T 45340827197,531385036815,6227630455564,72986367133614,

%U 855377894814551,10024792297748632,117487669001323549,1376922218413007325

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

%C Column 3 of A239819

%H R. H. Hardin, <a href="/A239814/b239814.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=4

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 27 2014