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A202964 Number of arrays of 4 integers in -n..n with sum zero and adjacent elements differing in absolute value.

%I A202964 #9 Jun 03 2018 07:57:50
%S A202964 4,28,108,268,544,972,1576,2392,3456,4792,6436,8424,10780,13540,16740,
%T A202964 20404,24568,29268,34528,40384,46872,54016,61852,70416,79732,89836,
%U A202964 100764,112540,125200,138780,153304,168808,185328,202888,221524,241272
%N A202964 Number of arrays of 4 integers in -n..n with sum zero and adjacent elements differing in absolute value.
%C A202964 Row 2 of A202962.
%H A202964 R. H. Hardin, <a href="/A202964/b202964.txt">Table of n, a(n) for n = 1..210</a>
%F A202964 Empirical: a(n) = 3*a(n-1) -3*a(n-2) +2*a(n-3) -3*a(n-4) +3*a(n-5) -a(n-6).
%F A202964 Empirical g.f.: 4*x*(1 + 4*x + 9*x^2 + 5*x^3 + 5*x^4) / ((1 - x)^4*(1 + x + x^2)). - _Colin Barker_, Jun 03 2018
%e A202964 Some solutions for n=5:
%e A202964 .-4....1...-1....0...-1....0....0....0....3...-2...-2...-5....0...-4....1...-5
%e A202964 ..5...-4....2...-4....0...-3...-1...-2...-4...-1....5....4....3....1...-2....1
%e A202964 ..2....1...-5....3....3....2....3....4...-2....5...-2....0....2....4....4....4
%e A202964 .-3....2....4....1...-2....1...-2...-2....3...-2...-1....1...-5...-1...-3....0
%Y A202964 Cf. A202962.
%K A202964 nonn
%O A202964 1,1
%A A202964 _R. H. Hardin_, Dec 26 2011