cp's OEIS Frontend

A252178 Number of length 2+2 0..n arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

%I A252178 #8 Dec 01 2018 12:02:25
%S A252178 12,49,132,285,536,917,1464,2217,3220,4521,6172,8229,10752,13805,
%T A252178 17456,21777,26844,32737,39540,47341,56232,66309,77672,90425,104676,
%U A252178 120537,138124,157557,178960,202461,228192,256289,286892,320145,356196,395197
%N A252178 Number of length 2+2 0..n arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.
%H A252178 R. H. Hardin, <a href="/A252178/b252178.txt">Table of n, a(n) for n = 1..210</a>
%F A252178 Empirical: a(n) = (1/6)*n^4 + (7/3)*n^3 + (29/6)*n^2 + (11/3)*n + 1.
%F A252178 Conjectures from _Colin Barker_, Dec 01 2018: (Start)
%F A252178 G.f.: x*(12 - 11*x + 7*x^2 - 5*x^3 + x^4) / (1 - x)^5.
%F A252178 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F A252178 (End)
%e A252178 Some solutions for n=6:
%e A252178 ..4....2....0....4....2....6....2....1....4....1....4....4....2....4....2....2
%e A252178 ..6....2....2....5....2....6....2....1....3....1....5....1....6....3....4....0
%e A252178 ..0....0....3....1....1....0....4....6....2....2....0....6....0....4....2....6
%e A252178 ..5....2....0....2....1....5....4....5....1....2....2....5....3....4....3....0
%Y A252178 Row 2 of A252177.
%K A252178 nonn
%O A252178 1,1
%A A252178 _R. H. Hardin_, Dec 15 2014