A183906 - OEIS

%I #8 Apr 05 2018 20:38:32

%S 2,5,17,38,67,105,153,212,283,367,465,578,707,853,1017,1200,1403,1627,

%T 1873,2142,2435,2753,3097,3468,3867,4295,4753,5242,5763,6317,6905,

%U 7528,8187,8883,9617,10390,11203,12057,12953,13892,14875,15903,16977,18098

%N Number of nondecreasing arrangements of n+2 numbers in 0..3 with each number being the sum mod 4 of two others.

%C Column 3 of A183912.

%H R. H. Hardin, <a href="/A183906/b183906.txt">Table of n, a(n) for n = 1..199</a>

%F Empirical: a(n) = (1/6)*n^3 + 2*n^2 + (5/6)*n - 8 for n>2.

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

%F G.f.: x*(2 - 3*x + 9*x^2 - 8*x^3 - x^4 + 2*x^5) / (1 - x)^4.

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>6.

%F (End)

%e All solutions for n=2:

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

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

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

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

%Y Cf. A183912.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 07 2011