cp's OEIS Frontend

A250647 Number of length 3+1 0..n arrays with the sum of the maximum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

%I A250647 #7 Nov 15 2018 12:50:20
%S A250647 6,23,44,89,134,219,296,433,550,751,916,1193,1414,1779,2064,2529,2886,
%T A250647 3463,3900,4601,5126,5963,6584,7569,8294,9439,10276,11593,12550,14051,
%U A250647 15136,16833,18054,19959,21324,23449,24966,27323,29000,31601,33446,36303
%N A250647 Number of length 3+1 0..n arrays with the sum of the maximum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.
%H A250647 R. H. Hardin, <a href="/A250647/b250647.txt">Table of n, a(n) for n = 1..210</a>
%F A250647 Empirical: a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 3*a(n-4) + 3*a(n-5) + a(n-6) - a(n-7).
%F A250647 Empirical for n mod 2 = 0: a(n) = (5/12)*n^3 + 3*n^2 + (10/3)*n + 1.
%F A250647 Empirical for n mod 2 = 1: a(n) = (5/12)*n^3 + (11/4)*n^2 + (31/12)*n + (1/4).
%F A250647 Empirical g.f.: x*(6 + 17*x + 3*x^2 - 6*x^3 + x^5 - x^6) / ((1 - x)^4*(1 + x)^3). - _Colin Barker_, Nov 15 2018
%e A250647 Some solutions for n=6:
%e A250647 ..0....5....1....6....1....0....0....0....2....3....4....6....1....2....4....0
%e A250647 ..0....0....2....2....0....0....3....0....2....0....0....5....5....0....2....0
%e A250647 ..5....0....0....3....3....2....0....3....2....3....2....1....0....1....2....5
%e A250647 ..1....5....0....1....4....1....6....1....4....6....2....1....0....1....0....2
%Y A250647 Row 3 of A250646.
%K A250647 nonn
%O A250647 1,1
%A A250647 _R. H. Hardin_, Nov 26 2014