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A199534 Number of -n..n arrays x(0..6) of 7 elements with zero sum and no two consecutive zero elements.

%I A199534 #9 May 16 2018 05:38:02
%S A199534 200,6346,53302,252154,860854,2378412,5662636,12071420,23627580,
%T A199534 43207238,74751754,123503206,196263418,301676536,450535152,656109976,
%U A199534 934503056,1305024546,1790593022,2418159346,3219154078,4229958436,5492398804
%N A199534 Number of -n..n arrays x(0..6) of 7 elements with zero sum and no two consecutive zero elements.
%C A199534 Row 7 of A199530.
%H A199534 R. H. Hardin, <a href="/A199534/b199534.txt">Table of n, a(n) for n = 1..200</a>
%F A199534 Empirical: a(n) = (5887/180)*n^6 + (5887/60)*n^5 + (620/9)*n^4 + (11/12)*n^3 + (433/180)*n^2 - (91/30)*n.
%F A199534 Conjectures from _Colin Barker_, May 16 2018: (Start)
%F A199534 G.f.: 2*x*(100 + 2473*x + 6540*x^2 + 2653*x^3 + 4*x^4 + 4*x^5) / (1 - x)^7.
%F A199534 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A199534 (End)
%e A199534 Some solutions for n=5:
%e A199534 .-5...-5...-4...-5...-4...-5...-4...-5...-4...-5...-5...-5...-5...-4...-5...-4
%e A199534 ..1...-3....1....3....0...-5...-4....4...-4....5...-3....0....5...-4....3....2
%e A199534 ..1....4...-1....0....4....2....0...-5...-1....1...-1...-2....3....1...-5....2
%e A199534 .-1...-2....3...-1....5...-2....5....5...-2....3...-1....4...-3....4....1....0
%e A199534 ..4...-4...-4....1...-2....5...-1....2....3...-3....5....1....0....4....5...-1
%e A199534 ..5....5....3...-2...-1....5...-1....0....3...-5....0....4...-2....1....5....1
%e A199534 .-5....5....2....4...-2....0....5...-1....5....4....5...-2....2...-2...-4....0
%Y A199534 Cf. A199530.
%K A199534 nonn
%O A199534 1,1
%A A199534 _R. H. Hardin_, Nov 07 2011