cp's OEIS Frontend

A221966 Number of -7..7 arrays of length n with the sum ahead of each element differing from the sum following that element by 7 or less.

%I A221966 #8 Aug 14 2018 08:57:20
%S A221966 15,225,1695,17025,159615,1535745,14661375,140355585,1342437375,
%T A221966 12843782145,122870296575,1175482548225,11245539966975,
%U A221966 107583628673025,1029227717656575,9846388295204865,94198150438322175,901172262043910145
%N A221966 Number of -7..7 arrays of length n with the sum ahead of each element differing from the sum following that element by 7 or less.
%C A221966 Column 7 of A221967.
%H A221966 R. H. Hardin, <a href="/A221966/b221966.txt">Table of n, a(n) for n = 1..67</a>
%F A221966 Empirical: a(n) = 7*a(n-1) + 32*a(n-2) - 56*a(n-3) - 160*a(n-4) + 112*a(n-5) + 256*a(n-6) - 64*a(n-7) - 128*a(n-8).
%F A221966 Empirical g.f.: 15*x*(1 + 2*x)*(1 - 2*x - 4*x^2)*(1 + 8*x - 16*x^2 - 8*x^3 + 16*x^4) / ((1 + x)*(1 - 2*x)*(1 + 2*x - 4*x^2)*(1 - 8*x - 16*x^2 + 8*x^3 + 16*x^4)). - _Colin Barker_, Aug 14 2018
%e A221966 Some solutions for n=6:
%e A221966 ..1....1...-7....0....1....0....0...-7....0....0....0....0....0....1....1....1
%e A221966 ..1....0....5....1....0....0....1....0...-4....0....0...-4....1....0....0....1
%e A221966 ..6....5...-2...-2...-3...-1....0....6....5...-2...-2....6...-4...-3...-2...-2
%e A221966 .-5...-2....0...-1....5...-1...-1...-4....1....6....2....4....3....3...-1....4
%e A221966 .-1...-4....1....7...-1....3...-2....3...-5....0....7...-4....1....4....6...-4
%e A221966 ..3....3....1...-1....4...-5....4...-7....5....0...-3....0....2...-1...-2....7
%Y A221966 Cf. A221967.
%K A221966 nonn
%O A221966 1,1
%A A221966 _R. H. Hardin_, Feb 01 2013