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Number of arrays of 14 nondecreasing integers in -n..n with sum zero and equal numbers greater than zero and less than zero
1

%I #5 Mar 31 2012 12:36:56

%S 8,36,280,1844,9880,43958,168314,568933,1734054,4842044,12545910,

%T 30469542,69935848,152731858,319150868,641127127,1243115122,

%U 2334434336,4258292458,7564553798,13115830616,22239519138,36942424868,60209406935

%N Number of arrays of 14 nondecreasing integers in -n..n with sum zero and equal numbers greater than zero and less than zero

%C Row 7 of A203291

%H R. H. Hardin, <a href="/A203297/b203297.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) -a(n-2) -3*a(n-3) +a(n-4) -a(n-5) +4*a(n-6) -3*a(n-7) +3*a(n-8) +3*a(n-9) -4*a(n-10) -2*a(n-11) -3*a(n-12) -2*a(n-13) +8*a(n-15) +7*a(n-17) -2*a(n-18) -a(n-19) -5*a(n-20) -13*a(n-21) +3*a(n-22) +a(n-23) +5*a(n-24) +6*a(n-25) +5*a(n-26) +a(n-27) +3*a(n-28) -13*a(n-29) -5*a(n-30) -a(n-31) -2*a(n-32) +7*a(n-33) +8*a(n-35) -2*a(n-37) -3*a(n-38) -2*a(n-39) -4*a(n-40) +3*a(n-41) +3*a(n-42) -3*a(n-43) +4*a(n-44) -a(n-45) +a(n-46) -3*a(n-47) -a(n-48) +3*a(n-49) -a(n-50)

%e Some solutions for n=3

%e .-2...-3...-3...-3...-3...-3...-3...-3...-3...-3...-2...-3...-2...-3...-3...-3

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

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

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

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

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

%e ..0....0....0....0....0....0....0....0....0...-1....0...-1...-1....0...-1....0

%e ..0....0....0....0....0....0....0....0....0....1....0....2....1....0....1....0

%e ..0....1....1....0....0....1....0....1....1....2....0....2....1....1....1....1

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

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

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

%e ..2....2....3....2....3....3....0....3....2....2....3....2....3....2....3....3

%e ..2....2....3....3....3....3....3....3....3....2....3....2....3....3....3....3

%K nonn

%O 1,1

%A _R. H. Hardin_ Dec 31 2011