A183910 - OEIS

%I #9 Apr 06 2018 10:07:39

%S 2,5,40,207,778,2199,5126,10501,19630,34274,56754,90071,138042,205453,

%T 298230,423629,590446,809248,1092626,1455471,1915274,2492451,3210694,

%U 4097349,5183822,6506014,8104786,10026455,12323322,15054233,18285174

%N Number of nondecreasing arrangements of n+2 numbers in 0..7 with each number being the sum mod 8 of two others.

%C Column 7 of A183912.

%H R. H. Hardin, <a href="/A183910/b183910.txt">Table of n, a(n) for n = 1..61</a>

%F Empirical: a(n) = (1/5040)*n^7 + (1/120)*n^6 + (53/360)*n^5 + (17/12)*n^4 - (1313/720)*n^3 - (1777/40)*n^2 + (14876/105)*n - 83 for n>3.

%F Conjectures from _Colin Barker_, Apr 06 2018: (Start)

%F G.f.: x*(2 - 11*x + 56*x^2 - 85*x^3 + 102*x^4 - 231*x^5 + 302*x^6 - 129*x^7 - 44*x^8 + 49*x^9 - 10*x^10) / (1 - x)^8.

%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>10.

%F (End)

%e All solutions for n=2:

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

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

%e ..0....4....6....4....4

%e ..0....6....6....4....4

%Y Cf. A183912.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 07 2011