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A201811
T(n,k)=Number of arrays of n integers in -k..k with sum zero and equal numbers of elements greater than zero and less than zero
11
1, 1, 3, 1, 5, 7, 1, 7, 13, 19, 1, 9, 19, 61, 51, 1, 11, 25, 151, 221, 141, 1, 13, 31, 313, 631, 1001, 393, 1, 15, 37, 571, 1401, 4621, 4145, 1107, 1, 17, 43, 949, 2651, 15681, 23857, 18733, 3139, 1, 19, 49, 1471, 4501, 42821, 90609, 164599, 82381, 8953, 1, 21, 55, 2161
OFFSET
1,3
COMMENTS
Table starts
....1......1.......1........1.........1..........1..........1...........1
....3......5.......7........9........11.........13.........15..........17
....7.....13......19.......25........31.........37.........43..........49
...19.....61.....151......313.......571........949.......1471........2161
...51....221.....631.....1401......2651.......4501.......7071.......10481
..141...1001....4621....15681.....42821......99961.....207621......394241
..393...4145...23857....90609....263201.....637393....1355145.....2613857
.1107..18733..164599...909945...3688091...12004357...33222463....81196529
.3139..82381..948871..6105913..27050251...93039589..266948431...668734321
.8953.375745.6359617.57290209.343631641.1554288913.5714583505.17932764577
LINKS
FORMULA
Empirical for rows:
T(1,k) = 1
T(2,k) = 2*k + 1
T(3,k) = 6*k + 1
T(4,k) = 4*k^3 + 14*k + 1
T(5,k) = 20*k^3 + 30*k + 1
T(6,k) = 11*k^5 + 65*k^3 + 64*k + 1
T(7,k) = 77*k^5 + 175*k^3 + 140*k + 1
T(8,k) = (302/9)*k^7 + (2912/9)*k^5 + (3878/9)*k^3 + 318*k + 1
T(9,k) = 302*k^7 + 1064*k^5 + 1022*k^3 + 750*k + 1
T(10,k) = (15619/144)*k^9 + (37465/24)*k^7 + (146209/48)*k^5 + (86705/36)*k^3 + 1828*k + 1
T(11,k) = (171809/144)*k^9 + (48785/8)*k^7 + (386155/48)*k^5 + (206635/36)*k^3 + 4576*k + 1
EXAMPLE
Some solutions for n=7 k=3
..0...-1...-3....2...-1...-2....3....0....1...-2....0....3...-2...-3....2...-3
.-1....1....1...-2....1....2....3....2...-1...-3...-2....0...-2....3....2....3
..2....0....0....3...-2...-2...-3....2....1....0....2...-3....0...-1...-1....2
..0....1....2...-3....2...-1....2...-2....0....3...-1...-1....1....1...-2...-3
..1...-3...-1....3...-2....0....0....2....1...-3....1...-3...-3....0....1...-1
..0....3....2...-3....0....2...-2...-2...-1....2....1....3....3....2...-2....0
.-2...-1...-1....0....2....1...-3...-2...-1....3...-1....1....3...-2....0....2
CROSSREFS
Column 1 is A002426
Row 2 is A004273(n+1)
Row 3 is A016921
Sequence in context: A209819 A193648 A221881 * A199898 A320904 A193844
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Dec 05 2011
STATUS
approved