cp's OEIS Frontend

A250421 Number of length 4+1 0..n arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

%I A250421 #8 Nov 14 2018 09:33:02
%S A250421 20,125,476,1351,3154,6433,11906,20461,33178,51359,76520,110417,
%T A250421 155080,212797,286144,378023,491638,630529,798614,1000157,1239806,
%U A250421 1522639,1854124,2240161,2687132,3201853,3791620,4464263,5228090,6091937,7065226
%N A250421 Number of length 4+1 0..n arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.
%H A250421 R. H. Hardin, <a href="/A250421/b250421.txt">Table of n, a(n) for n = 1..210</a>
%F A250421 Empirical: a(n) = 4*a(n-1) - 6*a(n-2) + 6*a(n-3) - 9*a(n-4) + 12*a(n-5) - 9*a(n-6) + 6*a(n-7) - 6*a(n-8) + 4*a(n-9) - a(n-10).
%F A250421 Empirical for n mod 3 = 0: a(n) = (2/15)*n^5 + (92/27)*n^4 + (85/27)*n^3 + (68/9)*n^2 + (68/15)*n + 1.
%F A250421 Empirical for n mod 3 = 1: a(n) = (2/15)*n^5 + (92/27)*n^4 + (85/27)*n^3 + (68/9)*n^2 + (632/135)*n + (29/27).
%F A250421 Empirical for n mod 3 = 2: a(n) = (2/15)*n^5 + (92/27)*n^4 + (85/27)*n^3 + (68/9)*n^2 + (652/135)*n + (31/27).
%F A250421 Empirical g.f.: x*(20 + 45*x + 96*x^2 + 77*x^3 + 36*x^4 - 48*x^5 - 44*x^6 - 37*x^7 - x^9) / ((1 - x)^6*(1 + x + x^2)^2). - _Colin Barker_, Nov 14 2018
%e A250421 Some solutions for n=6:
%e A250421 ..6....6....6....6....6....4....1....1....3....1....5....6....3....3....2....2
%e A250421 ..3....1....1....4....3....5....0....6....0....1....6....3....0....6....2....0
%e A250421 ..5....0....1....6....4....1....6....0....5....2....4....6....6....1....4....6
%e A250421 ..3....1....4....4....0....4....4....6....0....1....6....1....5....1....3....1
%e A250421 ..6....4....3....5....6....2....4....1....0....1....5....3....6....5....6....3
%Y A250421 Row 4 of A250419.
%K A250421 nonn
%O A250421 1,1
%A A250421 _R. H. Hardin_, Nov 22 2014