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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. 1

%I

%S 200,6346,53302,252154,860854,2378412,5662636,12071420,23627580,

%T 43207238,74751754,123503206,196263418,301676536,450535152,656109976,

%U 934503056,1305024546,1790593022,2418159346,3219154078,4229958436,5492398804

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

%C Row 7 of A199530.

%H R. H. Hardin, <a href="/A199534/b199534.txt">Table of n, a(n) for n = 1..200</a>

%F 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 Conjectures from _Colin Barker_, May 16 2018: (Start)

%F G.f.: 2*x*(100 + 2473*x + 6540*x^2 + 2653*x^3 + 4*x^4 + 4*x^5) / (1 - x)^7.

%F 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 (End)

%e Some solutions for n=5:

%e .-5...-5...-4...-5...-4...-5...-4...-5...-4...-5...-5...-5...-5...-4...-5...-4

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

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

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

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

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

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

%Y Cf. A199530.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 07 2011

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Last modified October 16 19:13 EDT 2021. Contains 348043 sequences. (Running on oeis4.)