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A240002 Number of 3 X n 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

%I A240002 #8 Oct 27 2018 06:21:35
%S A240002 12,61,190,526,1262,2766,5647,10878,19971,35180,59780,98414,157524,
%T A240002 245879,375214,560995,823326,1188015,1687817,2363873,3267365,4461408,
%U A240002 6023201,8046460,10644157,13951590,18129810,23369432,29894858,37968941
%N A240002 Number of 3 X n 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.
%H A240002 R. H. Hardin, <a href="/A240002/b240002.txt">Table of n, a(n) for n = 1..210</a>
%F A240002 Empirical: a(n) = (1/40320)*n^8 + (1/2016)*n^7 + (7/576)*n^6 + (17/360)*n^5 + (6367/5760)*n^4 - (935/288)*n^3 + (28145/672)*n^2 - (114913/840)*n + 237 for n>6.
%F A240002 Conjectures from _Colin Barker_, Oct 27 2018: (Start)
%F A240002 G.f.: x*(12 - 47*x + 73*x^2 + 4*x^3 - 244*x^4 + 558*x^5 - 737*x^6 + 651*x^7 - 375*x^8 + 86*x^9 + 91*x^10 - 128*x^11 + 80*x^12 - 27*x^13 + 4*x^14) / (1 - x)^9.
%F A240002 a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>15.
%F A240002 (End)
%e A240002 Some solutions for n=5:
%e A240002 ..0..3..3..0..0....0..3..3..0..0....0..0..0..0..3....0..3..3..0..0
%e A240002 ..0..3..3..1..3....0..0..3..1..3....0..3..3..0..0....0..3..2..3..3
%e A240002 ..0..3..3..2..0....0..0..2..1..2....0..0..2..1..3....0..3..1..0..2
%Y A240002 Row 3 of A240000.
%K A240002 nonn
%O A240002 1,1
%A A240002 _R. H. Hardin_, Mar 30 2014