A183899 - OEIS

%I #8 Apr 05 2018 10:27:10

%S 1,5,66,174,329,539,815,1169,1614,2164,2834,3640,4599,5729,7049,8579,

%T 10340,12354,14644,17234,20149,23415,27059,31109,35594,40544,45990,

%U 51964,58499,65629,73389,81815,90944,100814,111464,122934,135265,148499,162679

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

%C Column 4 of A183904.

%H R. H. Hardin, <a href="/A183899/b183899.txt">Table of n, a(n) for n = 1..62</a>

%F Empirical: a(n) = (1/24)*n^4 + (11/12)*n^3 + (179/24)*n^2 + (199/12)*n - 81 for n>3.

%F Conjectures from _Colin Barker_, Apr 05 2018: (Start)

%F 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 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 (End)

%e All solutions for n=2:

%e ..0....0....0....0....0

%e ..1....1....2....1....0

%e ..3....2....3....1....0

%e ..3....2....4....2....0

%e ..4....4....4....3....0

%Y Cf. A183904.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 07 2011