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.

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

Author

R. H. Hardin Nov 07 2011

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1096

Crossrefs

Column 1 is A102881

Row 3 is A028896

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