cp's OEIS Frontend

A200759 Number of 0..3 arrays x(0..n-1) of n elements with nondecreasing average value.

%I A200759 #16 Jul 22 2025 15:54:23
%S A200759 4,10,23,51,110,233,488,1013,2088,4278,8720,17695,35768,72054,144717,
%T A200759 289887,579312,1155257,2299426,4568935,9064316,17957296,35529320,
%U A200759 70213565,138607340,273351142,538591471,1060310343,2085784818,4100099321
%N A200759 Number of 0..3 arrays x(0..n-1) of n elements with nondecreasing average value.
%C A200759 Column 3 of A200763
%H A200759 R. H. Hardin, <a href="/A200759/b200759.txt">Table of n, a(n) for n = 1..174</a>
%F A200759 Empirical: a(n) = 5*a(n-1) -8*a(n-2) +3*a(n-3) +3*a(n-4) -2*a(n-5) +a(n-6) -3*a(n-7) +2*a(n-8) -a(n-9) +a(n-10).
%F A200759 Empirical g.f.: -x*(4-10*x+5*x^2+4*x^3-3*x^4-3*x^6+x^9+2*x^7-x^8) / ( (x-1)*(x^3+x^2+x-1)*(x^6-x^5+2*x^4-x^3-2*x^2+3*x-1) ). - _R. J. Mathar_, Nov 22 2011
%e A200759 Some solutions for n=8
%e A200759 ..0....0....1....0....0....0....0....0....1....0....0....0....0....0....0....0
%e A200759 ..0....0....1....3....0....0....2....0....2....0....0....0....0....2....2....0
%e A200759 ..0....0....1....3....3....2....1....1....2....3....1....0....1....3....1....0
%e A200759 ..0....2....1....2....2....2....1....1....2....3....1....3....2....2....2....3
%e A200759 ..0....2....1....2....2....3....1....1....2....2....3....1....1....3....3....1
%e A200759 ..0....2....2....2....3....3....2....3....3....3....3....2....3....3....2....2
%e A200759 ..1....1....3....2....2....2....2....1....3....2....3....1....2....3....2....1
%e A200759 ..3....3....3....2....2....2....2....1....3....2....3....3....2....3....3....1
%K A200759 nonn
%O A200759 1,1
%A A200759 _R. H. Hardin_, Nov 22 2011