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A200195 Number of -n..n arrays x(0..5) of 6 elements with zero sum, adjacent elements differing by more than one, and elements alternately increasing and decreasing. 1

%I #9 May 20 2018 11:32:57

%S 2,54,482,2240,7266,18838,41938,83600,153278,263198,428718,668684,

%T 1005790,1466934,2083578,2892104,3934174,5257082,6914122,8964936,

%U 11475878,14520370,18179258,22541172,27702886,33769670,40855654,49084180

%N Number of -n..n arrays x(0..5) of 6 elements with zero sum, adjacent elements differing by more than one, and elements alternately increasing and decreasing.

%C Row 6 of A200192.

%H R. H. Hardin, <a href="/A200195/b200195.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +2*a(n-5) -a(n-6) -a(n-7) +2*a(n-8) -a(n-10) -2*a(n-11) +3*a(n-12) -a(n-13).

%F Empirical g.f.: 2*x*(1 + 24*x + 162*x^2 + 452*x^3 + 782*x^4 + 999*x^5 + 1045*x^6 + 910*x^7 + 622*x^8 + 292*x^9 + 74*x^10 + 5*x^11) / ((1 - x)^6*(1 + x)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)). - _Colin Barker_, May 20 2018

%e Some solutions for n=5:

%e ..1...-5...-5....3...-4....0....0...-2...-3....2....4....3...-4...-4...-1....0

%e .-5....0....4...-2....3...-5...-3....1...-1...-1...-4...-3....4....5...-3....4

%e ..0...-5...-3....3...-1....4....5...-5...-4....4....4....3...-3...-5....5...-3

%e .-4....5....5...-4....4...-3...-3....5....4...-4...-4...-3....0....3...-5...-1

%e ..5....1...-2....1...-5....3....3...-1...-1....3....1....5...-2...-2....5...-4

%e ..3....4....1...-1....3....1...-2....2....5...-4...-1...-5....5....3...-1....4

%Y Cf. A200192.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 14 2011

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