cp's OEIS Frontend

A201815 Number of arrays of 7 integers in -n..n with sum zero and equal numbers of elements greater than zero and less than zero.

%I A201815 #9 May 25 2018 11:13:36
%S A201815 393,4145,23857,90609,263201,637393,1355145,2613857,4675609,7876401,
%T A201815 12635393,19464145,28975857,41894609,59064601,81459393,110191145,
%U A201815 146519857,191862609,247802801,316099393,398696145,497730857,615544609
%N A201815 Number of arrays of 7 integers in -n..n with sum zero and equal numbers of elements greater than zero and less than zero.
%C A201815 Row 7 of A201811.
%H A201815 R. H. Hardin, <a href="/A201815/b201815.txt">Table of n, a(n) for n = 1..210</a>
%F A201815 Empirical: a(n) = 77*n^5 + 175*n^3 + 140*n + 1.
%F A201815 Conjectures from _Colin Barker_, May 25 2018: (Start)
%F A201815 G.f.: x*(393 + 1787*x + 4882*x^2 + 1782*x^3 + 397*x^4 - x^5) / (1 - x)^6.
%F A201815 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 A201815 (End)
%e A201815 Some solutions for n=4.
%e A201815 ..1....3....0....1....4...-4...-4....3...-2....0....2....2...-3....4....4....4
%e A201815 ..2....1...-3...-1....3....4....1...-3....0....1...-3...-3....2....3...-3....1
%e A201815 ..0...-3...-4...-2...-4....4....4...-3....1....4....0...-1...-3....0....0...-2
%e A201815 ..4....0....4...-3...-4...-3...-3....3...-4...-2....2....1....0....2....0...-3
%e A201815 .-3...-2...-3....3....4....0....4....0....3...-1...-1....0....3...-3....0...-4
%e A201815 .-1...-2....2....2...-3....1....0...-1....4....1...-1...-3...-2...-2...-3....0
%e A201815 .-3....3....4....0....0...-2...-2....1...-2...-3....1....4....3...-4....2....4
%Y A201815 Cf. A201811.
%K A201815 nonn
%O A201815 1,1
%A A201815 _R. H. Hardin_, Dec 05 2011