A239987 - OEIS

%I #8 Oct 27 2018 06:21:00

%S 3,6,13,22,38,65,107,169,257,378,540,752,1024,1367,1793,2315,2947,

%T 3704,4602,5658,6890,8317,9959,11837,13973,16390,19112,22164,25572,

%U 29363,33565,38207,43319,48932,55078,61790,69102,77049,85667,94993,105065

%N 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 R. H. Hardin, <a href="/A239987/b239987.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/24)*n^4 - (1/4)*n^3 + (71/24)*n^2 - (43/4)*n + 23 for n>3.

%F Conjectures from _Colin Barker_, Oct 27 2018: (Start)

%F 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 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 (End)

%e Some solutions for n=4:

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

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

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

%Y Row 3 of A239986.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 30 2014