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A183899 Number of nondecreasing arrangements of n+3 numbers in 0..4 with each number being the sum mod 5 of three others.

%I A183899 #8 Apr 05 2018 10:27:10
%S A183899 1,5,66,174,329,539,815,1169,1614,2164,2834,3640,4599,5729,7049,8579,
%T A183899 10340,12354,14644,17234,20149,23415,27059,31109,35594,40544,45990,
%U A183899 51964,58499,65629,73389,81815,90944,100814,111464,122934,135265,148499,162679
%N A183899 Number of nondecreasing arrangements of n+3 numbers in 0..4 with each number being the sum mod 5 of three others.
%C A183899 Column 4 of A183904.
%H A183899 R. H. Hardin, <a href="/A183899/b183899.txt">Table of n, a(n) for n = 1..62</a>
%F A183899 Empirical: a(n) = (1/24)*n^4 + (11/12)*n^3 + (179/24)*n^2 + (199/12)*n - 81 for n>3.
%F A183899 Conjectures from _Colin Barker_, Apr 05 2018: (Start)
%F A183899 G.f.: x*(1 + 51*x^2 - 116*x^3 + 74*x^4 - 2*x^5 - 5*x^6 - 2*x^7) / (1 - x)^5.
%F A183899 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>8.
%F A183899 (End)
%e A183899 All solutions for n=2:
%e A183899 ..0....0....0....0....0
%e A183899 ..1....1....2....1....0
%e A183899 ..3....2....3....1....0
%e A183899 ..3....2....4....2....0
%e A183899 ..4....4....4....3....0
%Y A183899 Cf. A183904.
%K A183899 nonn
%O A183899 1,2
%A A183899 _R. H. Hardin_, Jan 07 2011