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A199530
T(n,k)=Number of -k..k arrays x(0..n-1) of n elements with zero sum and no two consecutive zero elements
11
1, 1, 2, 1, 4, 6, 1, 6, 18, 12, 1, 8, 36, 72, 32, 1, 10, 60, 212, 320, 80, 1, 12, 90, 464, 1324, 1414, 200, 1, 14, 126, 860, 3734, 8342, 6346, 520, 1, 16, 168, 1432, 8470, 30484, 53302, 28766, 1336, 1, 18, 216, 2212, 16682, 84852, 252154, 343710, 131246, 3472, 1, 20, 270
OFFSET
1,3
COMMENTS
Table starts
....1......1........1.........1.........1..........1...........1...........1
....2......4........6.........8........10.........12..........14..........16
....6.....18.......36........60........90........126.........168.........216
...12.....72......212.......464.......860.......1432........2212........3232
...32....320.....1324......3734......8470......16682.......29750.......49284
...80...1414.....8342.....30484.....84852.....197962......407946......766664
..200...6346....53302....252154....860854....2378412.....5662636....12071420
..520..28766...343710...2105064...8815392...28844590....79345982...191873280
.1336.131246..2232322..17701326..90927530..352355640..1119873360..3071898666
.3472.602390.14582218.149708146.943302430.4329146404.15897133212.49465959068
LINKS
FORMULA
Empirical for rows:
T(1,k) = 1
T(2,k) = 2*k
T(3,k) = 3*k^2 + 3*k
T(4,k) = (16/3)*k^3 + 8*k^2 - (4/3)*k
T(5,k) = (115/12)*k^4 + (115/6)*k^3 + (41/12)*k^2 - (1/6)*k
T(6,k) = (88/5)*k^5 + 44*k^4 + (58/3)*k^3 - 3*k^2 + (31/15)*k
T(7,k) = (5887/180)*k^6 + (5887/60)*k^5 + (620/9)*k^4 + (11/12)*k^3 + (433/180)*k^2 - (91/30)*k
EXAMPLE
Some solutions for n=6 k=5
..1...-1....0...-4...-1....4....1...-5....1....2...-1....1....3....3....1....5
..0...-1...-1...-3....0....5...-3....0....1...-3...-3...-4....2...-5....1....2
.-4....5....3...-1...-2...-3....5....1...-1....5....0....2...-3....4...-4...-5
..3...-2...-3....2....2...-4...-1....2...-4....4...-2....2....2...-5....5...-1
..1...-3...-2....4...-4...-4....0....5....2...-5....5....4...-4....0...-2....1
.-1....2....3....2....5....2...-2...-3....1...-3....1...-5....0....3...-1...-2
CROSSREFS
Column 1 is A102881
Row 3 is A028896
Sequence in context: A033877 A059369 A369518 * A208765 A232335 A098473
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Nov 07 2011
STATUS
approved