cp's OEIS Frontend

A250168 Number of length 3+1 0..n arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.

%I A250168 #8 Nov 12 2018 14:37:37
%S A250168 8,37,96,211,380,639,976,1437,2000,2721,3568,4607,5796,7211,8800,
%T A250168 10649,12696,15037,17600,20491,23628,27127,30896,35061,39520,44409,
%U A250168 49616,55287,61300,67811,74688,82097,89896,98261,107040,116419,126236,136687,147600
%N A250168 Number of length 3+1 0..n arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.
%H A250168 R. H. Hardin, <a href="/A250168/b250168.txt">Table of n, a(n) for n = 1..210</a>
%F A250168 Empirical: a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).
%F A250168 Empirical for n mod 2 = 0: a(n) = (29/12)*n^3 + (11/4)*n^2 + (17/6)*n + 1.
%F A250168 Empirical for n mod 2 = 1: a(n) = (29/12)*n^3 + (11/4)*n^2 + (19/12)*n + (5/4).
%F A250168 Empirical g.f.: x*(8 + 21*x + 14*x^2 + 14*x^3 + 2*x^4 - x^5) / ((1 - x)^4*(1 + x)^2). - _Colin Barker_, Nov 12 2018
%e A250168 Some solutions for n=6:
%e A250168 ..4....0....3....6....1....1....6....2....0....5....0....1....4....0....4....0
%e A250168 ..5....2....3....1....4....2....5....2....3....5....1....3....1....3....0....3
%e A250168 ..5....5....4....1....5....3....0....4....5....3....6....0....5....1....5....4
%e A250168 ..6....6....3....6....3....5....6....6....0....5....2....1....6....0....4....6
%Y A250168 Row 3 of A250167.
%K A250168 nonn
%O A250168 1,1
%A A250168 _R. H. Hardin_, Nov 13 2014