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

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

R. H. Hardin, Table of n, a(n) for n = 1..9999

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

Adjacent sequences: A201808 A201809 A201810 * A201812 A201813 A201814

Keyword

nonn,tabl

Author

R. H. Hardin Dec 05 2011

Status

approved