cp's OEIS Frontend

A240001 Number of 2 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 A240001 #8 Oct 27 2018 06:21:06
%S A240001 5,13,25,42,65,95,133,180,237,305,385,478,585,707,845,1000,1173,1365,
%T A240001 1577,1810,2065,2343,2645,2972,3325,3705,4113,4550,5017,5515,6045,
%U A240001 6608,7205,7837,8505,9210,9953,10735,11557,12420,13325,14273,15265,16302
%N A240001 Number of 2 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 A240001 R. H. Hardin, <a href="/A240001/b240001.txt">Table of n, a(n) for n = 1..210</a>
%F A240001 Empirical: a(n) = (1/6)*n^3 + 1*n^2 + (23/6)*n.
%F A240001 Conjectures from _Colin Barker_, Oct 27 2018: (Start)
%F A240001 G.f.: x*(5 - 7*x + 3*x^2) / (1 - x)^4.
%F A240001 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
%F A240001 (End)
%e A240001 Some solutions for n=5:
%e A240001 ..0..0..0..0..0....0..0..3..3..0....0..0..0..0..3....0..0..0..0..0
%e A240001 ..3..3..0..0..0....0..0..3..2..3....0..0..0..3..3....0..0..0..0..3
%Y A240001 Row 2 of A240000.
%K A240001 nonn
%O A240001 1,1
%A A240001 _R. H. Hardin_, Mar 30 2014