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A221963 Number of -4..4 arrays of length n with the sum ahead of each element differing from the sum following that element by 4 or less. 1

%I

%S 9,81,369,2241,12609,73089,419841,2419713,13930497,80230401,462012417,

%T 2660655105,15322038273,88236228609,508131934209,2926215692289,

%U 16851403538433,97043367329793,558850475294721,3218291629752321

%N Number of -4..4 arrays of length n with the sum ahead of each element differing from the sum following that element by 4 or less.

%C Column 4 of A221967.

%H R. H. Hardin, <a href="/A221963/b221963.txt">Table of n, a(n) for n = 1..82</a>

%F Empirical: a(n) = 5*a(n-1) + 8*a(n-2) - 20*a(n-3) - 8*a(n-4) + 16*a(n-5).

%F Empirical g.f.: 9*x*(1 - 2*x)*(1 + 6*x - 8*x^3) / ((1 - x)*(1 + 2*x)*(1 - 6*x + 8*x^3)). - _Colin Barker_, Aug 11 2018

%e Some solutions for n=6:

%e .-3...-2....3....2....3...-4....1....1....2....0....0...-1...-3...-4...-2....0

%e ..4....1....3...-1...-3....1...-3....0...-2....1...-3....4....1...-2....4....3

%e .-3....1...-4...-2....2....4....2....3....0...-4...-2...-4....2....4...-2...-2

%e ..1...-3...-3....2....3...-4....1....0....1...-1....4....1....1...-1...-2...-1

%e .-2....3....4....1...-4....3...-1....0...-3....3...-2....2...-3....0....3....1

%e ..2...-3....2...-2....2...-3....2....1....2...-2...-1...-2....0...-3....1....0

%Y Cf. A221967.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 01 2013

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Last modified September 22 21:04 EDT 2021. Contains 347608 sequences. (Running on oeis4.)