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A200944 Number of 0..n arrays x(0..4) of 5 elements with nondecreasing average value and 0..n occur with instance counts within one of each other.

%I A200944 #12 Apr 21 2021 13:03:05
%S A200944 2,9,17,8,44,151,398,890,1774,3246,5555,9016,14012,21005,30529,43228,
%T A200944 59824,81159,108166,141927,183608,234553,296197,370168,458195,562234,
%U A200944 684319,826757,991940,1182536,1401309,1651348,1935801,2258191,2622105
%N A200944 Number of 0..n arrays x(0..4) of 5 elements with nondecreasing average value and 0..n occur with instance counts within one of each other.
%C A200944 Row 5 of A200942.
%H A200944 R. H. Hardin, <a href="/A200944/b200944.txt">Table of n, a(n) for n = 1..210</a>
%F A200944 Empirical: a(n) = 2*a(n-2) +2*a(n-3) -a(n-4) -3*a(n-5) -a(n-6) +a(n-8) +a(n-9) +a(n-10) -a(n-11) -a(n-12) +a(n-13) +a(n-14) +a(n-15) -a(n-17) -3*a(n-18) -a(n-19) +2*a(n-20) +2*a(n-21) -a(n-23) for n>26.
%F A200944 Empirical g.f.: 2*x +9*x^2 +17*x^3 +x^4*(8+44*x +135*x^2+294*x^3 +508*x^4+744*x^5 +961*x^6+1122*x^7 +1203*x^8+1200*x^9 +1118*x^10+955*x^11 +734*x^12+496*x^13 +289*x^14+128*x^15 +35*x^16+x^17) / ( (x^2+1)*(x^4+x^3+x^2+x+1)*(x^4+1)*(1+x+x^2)^2*(1+x)^3*(x-1)^6 ). - R. J. Mathar, Nov 25 2011
%e A200944 Some solutions for n=8
%e A200944 ..0....0....0....0....0....1....0....1....0....1....0....0....0....0....1....2
%e A200944 ..2....2....1....1....2....2....2....2....2....2....4....4....5....1....2....4
%e A200944 ..7....7....3....8....1....8....3....5....1....5....2....5....3....3....5....5
%e A200944 ..3....4....2....5....6....4....4....4....4....7....7....3....6....4....6....6
%e A200944 ..4....5....6....7....8....7....5....3....7....8....5....8....4....2....8....7
%Y A200944 Cf. A200942.
%K A200944 nonn
%O A200944 1,1
%A A200944 _R. H. Hardin_ Nov 24 2011