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A200943 Number of 0..n arrays x(0..3) of 4 elements with nondecreasing average value and 0..n occur with instance counts within one of each other.

%I A200943 #10 Jul 22 2025 16:01:38
%S A200943 1,7,3,15,46,107,213,383,636,997,1492,2151,3005,4092,5447,7114,9135,
%T A200943 11559,14433,17814,21753,26313,31552,37538,44334,52016,60651,70321,
%U A200943 81100,93075,106325,120945,137018,154645,173916,194937,217803,242628,269511
%N A200943 Number of 0..n arrays x(0..3) of 4 elements with nondecreasing average value and 0..n occur with instance counts within one of each other.
%C A200943 Row 4 of A200942
%H A200943 R. H. Hardin, <a href="/A200943/b200943.txt">Table of n, a(n) for n = 1..210</a>
%F A200943 Empirical: a(n) = 2*a(n-1) +a(n-2) -3*a(n-3) -a(n-4) +a(n-5) +3*a(n-6) -a(n-7) -2*a(n-8) +a(n-9) for n>11
%F A200943 Empirical g.f.: x+7x^2 -x^3*(3+9*x+13*x^2+x^4+9*x^3) / ( (1+x+x^2)*(1+x)^2*(x-1)^5 ). - R. J. Mathar, Nov 25 2011
%e A200943 Some solutions for n=8
%e A200943 ..1....1....0....1....0....0....1....2....1....3....1....2....4....0....0....1
%e A200943 ..7....3....1....2....1....1....4....5....6....7....4....4....5....2....2....4
%e A200943 ..6....2....2....3....5....6....5....4....4....5....5....7....8....8....4....6
%e A200943 ..8....4....5....8....4....7....6....8....8....8....7....8....7....4....8....8
%K A200943 nonn
%O A200943 1,2
%A A200943 _R. H. Hardin_ Nov 24 2011