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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 (list; table; graph; refs; listen; history; text; internal format)
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

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

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: A208759 A033877 A059369 * A208765 A232335 A098473

Adjacent sequences:  A199527 A199528 A199529 * A199531 A199532 A199533

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Nov 07 2011

STATUS

approved

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Last modified October 14 00:30 EDT 2019. Contains 327991 sequences. (Running on oeis4.)