A239844 - OEIS

%I #9 Oct 26 2018 11:20:02

%S 3,8,17,35,64,109,176,272,405,584,819,1121,1502,1975,2554,3254,4091,

%T 5082,6245,7599,9164,10961,13012,15340,17969,20924,24231,27917,32010,

%U 36539,41534,47026,53047,59630,66809,74619,83096,92277,102200,112904,124429

%N Number of n X 2 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it or two plus the sum of the elements diagonally to its northwest, modulo 4.

%H R. H. Hardin, <a href="/A239844/b239844.txt">Table of n, a(n) for n = 1..210</a>

%H W. Kuszmaul, <a href="http://arxiv.org/abs/1509.08216">Fast Algorithms for Finding Pattern Avoiders and Counting Pattern Occurrences in Permutations</a>, arXiv preprint arXiv:1509.08216, 2015

%F Empirical: a(n) = (1/24)*n^4 + (1/12)*n^3 + (11/24)*n^2 + (53/12)*n - 6 for n>2.

%F Conjectures from _Colin Barker_, Oct 26 2018: (Start)

%F G.f.: x*(1 - x + x^2)*(3 - 4*x + 4*x^3 - 2*x^4) / (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>7.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Column 2 of A239849.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 28 2014