A250420 - OEIS

%I #8 Nov 14 2018 07:18:43

%S 10,38,99,205,370,606,927,1345,1874,2526,3315,4253,5354,6630,8095,

%T 9761,11642,13750,16099,18701,21570,24718,28159,31905,35970,40366,

%U 45107,50205,55674,61526,67775,74433,81514,89030,96995,105421,114322,123710,133599

%N Number of length 3+1 0..n arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

%H R. H. Hardin, <a href="/A250420/b250420.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5).

%F Empirical for n mod 2 = 0: a(n) = (13/6)*n^3 + (13/4)*n^2 + (10/3)*n + 1.

%F Empirical for n mod 2 = 1: a(n) = (13/6)*n^3 + (13/4)*n^2 + (10/3)*n + (5/4).

%F Empirical g.f.: x*(10 + 8*x + 5*x^2 + 4*x^3 - x^4) / ((1 - x)^4*(1 + x)). - _Colin Barker_, Nov 14 2018

%e Some solutions for n=6:

%e ..0....4....3....5....0....2....4....0....5....0....4....1....2....4....5....1

%e ..2....2....1....2....5....4....2....0....0....4....4....1....2....6....4....0

%e ..0....2....1....4....2....4....5....1....3....1....4....2....5....2....6....3

%e ..5....0....0....4....4....2....4....0....0....4....0....3....0....6....0....0

%Y Row 3 of A250419.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 22 2014