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A239987 Number of 3 X n 0..3 arrays with no element equal to zero 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 A239987 #8 Oct 27 2018 06:21:00
%S A239987 3,6,13,22,38,65,107,169,257,378,540,752,1024,1367,1793,2315,2947,
%T A239987 3704,4602,5658,6890,8317,9959,11837,13973,16390,19112,22164,25572,
%U A239987 29363,33565,38207,43319,48932,55078,61790,69102,77049,85667,94993,105065
%N A239987 Number of 3 X n 0..3 arrays with no element equal to zero 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 A239987 R. H. Hardin, <a href="/A239987/b239987.txt">Table of n, a(n) for n = 1..210</a>
%F A239987 Empirical: a(n) = (1/24)*n^4 - (1/4)*n^3 + (71/24)*n^2 - (43/4)*n + 23 for n>3.
%F A239987 Conjectures from _Colin Barker_, Oct 27 2018: (Start)
%F A239987 G.f.: x*(3 - 9*x + 13*x^2 - 13*x^3 + 13*x^4 - 8*x^5 + x^6 + x^7) / (1 - x)^5.
%F A239987 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>8.
%F A239987 (End)
%e A239987 Some solutions for n=4:
%e A239987 ..3..0..0..0....3..0..0..0....3..0..0..0....3..0..0..0....3..0..0..0
%e A239987 ..2..3..0..3....2..1..0..0....3..1..3..0....3..1..3..0....2..1..0..0
%e A239987 ..2..0..1..0....2..0..0..0....3..2..3..1....3..1..2..3....2..0..3..3
%Y A239987 Row 3 of A239986.
%K A239987 nonn
%O A239987 1,1
%A A239987 _R. H. Hardin_, Mar 30 2014