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A223069 Number of n X 2 0..3 arrays with successive rows and columns fitting to straight lines with nondecreasing slope, with a single point array taken as having zero slope.

%I A223069 #8 Feb 18 2018 10:02:57
%S A223069 16,150,1080,6627,36552,187000,905440,4206453,18933408,83153850,
%T A223069 358250280,1520208679,6373759384,26468569500,109080982800,
%U A223069 446806304505,1821267503280,7395000190750,29933239010200,120863093617131
%N A223069 Number of n X 2 0..3 arrays with successive rows and columns fitting to straight lines with nondecreasing slope, with a single point array taken as having zero slope.
%C A223069 Column 2 of A223071.
%H A223069 R. H. Hardin, <a href="/A223069/b223069.txt">Table of n, a(n) for n = 1..41</a>
%F A223069 Empirical: a(n) = 16*a(n-1) -106*a(n-2) +376*a(n-3) -769*a(n-4) +904*a(n-5) -564*a(n-6) +144*a(n-7).
%F A223069 Empirical g.f.: x*(16 - 106*x + 376*x^2 - 769*x^3 + 904*x^4 - 564*x^5 + 144*x^6) / ((1 - x)^2*(1 - 2*x)^2*(1 - 3*x)^2*(1 - 4*x)). - _Colin Barker_, Feb 18 2018
%e A223069 Some solutions for n=3:
%e A223069 ..2..1....2..2....3..1....3..3....2..0....2..2....3..0....3..2....1..1....2..0
%e A223069 ..1..2....2..2....2..2....3..3....2..1....2..2....3..2....3..2....2..3....3..2
%e A223069 ..0..2....2..2....0..2....0..3....3..2....3..3....0..3....0..0....0..1....1..1
%K A223069 nonn
%O A223069 1,1
%A A223069 _R. H. Hardin_; Mar 14 2013