A222993 - OEIS

%I #10 Jun 17 2022 15:54:04

%S 9,50,222,867,3123,10660,35064,112373,353517,1097430,3374226,10302919,

%T 31301991,94757960,286108908,862258905,2595165345,7803321850,

%U 23447714310,70422834731,211436276379,634661150700,1904721649632,5715708452797

%N Number of n X 2 0..2 arrays with successive rows and columns fitting to straight lines with nondecreasing slope, with a single point array taken as having zero slope

%C Column 2 of A222996.

%C A353047 is probably equal to 12 times this sequence. - _N. J. A. Sloane_, Jun 17 2022

%H R. H. Hardin, <a href="/A222993/b222993.txt">Table of n, a(n) for n = 1..33</a>

%F Empirical: a(n) = 9*a(n-1) - 31*a(n-2) + 51*a(n-3) - 40*a(n-4) + 12*a(n-5).

%F Conjectures from _Colin Barker_, Feb 19 2018: (Start)

%F G.f.: x*(9 - 31*x + 51*x^2 - 40*x^3 + 12*x^4) / ((1 - x)^2*(1 - 2*x)^2*(1 - 3*x)).

%F a(n) = (-13 - 2^(6+n) + 3^(4+n) - 2*(1+2^(4+n))*n) / 4.

%F (End)

%e Some solutions for n=3:

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 11 2013