cp's OEIS Frontend

A221968 Number of -n..n arrays of length 5 with the sum ahead of each element differing from the sum following that element by n or less.

%I A221968 #8 Aug 14 2018 08:57:28
%S A221968 63,705,3647,12609,34111,78273,159615,297857,518719,854721,1345983,
%T A221968 2041025,2997567,4283329,5976831,8168193,10959935,14467777,18821439,
%U A221968 24165441,30659903,38481345,47823487,58898049,71935551,87186113
%N A221968 Number of -n..n arrays of length 5 with the sum ahead of each element differing from the sum following that element by n or less.
%C A221968 Row 5 of A221967.
%H A221968 R. H. Hardin, <a href="/A221968/b221968.txt">Table of n, a(n) for n = 1..63</a>
%F A221968 Empirical: a(n) = (20/3)*n^5 + (50/3)*n^4 + 20*n^3 + (40/3)*n^2 + (16/3)*n + 1.
%F A221968 Conjectures from _Colin Barker_, Aug 14 2018: (Start)
%F A221968 G.f.: x*(9 + 12*x - x^2)*(7 + 27*x + 5*x^2 + x^3) / (1 - x)^6.
%F A221968 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
%F A221968 (End)
%e A221968 Some solutions for n=6:
%e A221968 .-5...-3...-4...-3....2...-2....6....4...-1....2....2....3...-6....0....1....5
%e A221968 ..2....3....3....5...-1...-3...-4...-5...-2...-2....2...-2....5...-1....0...-6
%e A221968 .-1...-1....2....1...-1....4....6....3....2....1...-5...-4...-1...-1...-1....5
%e A221968 ..2....6....0....1....2...-3...-5....1...-4....4....3....3...-4....0....2...-5
%e A221968 .-3...-3...-5...-2...-2...-1....5...-3...-2....1....3....1....1...-1....2....3
%Y A221968 Cf. A221967.
%K A221968 nonn
%O A221968 1,1
%A A221968 _R. H. Hardin_, Feb 01 2013