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A201811
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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
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11
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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
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OFFSET
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1,3
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COMMENTS
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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
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..9999
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FORMULA
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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
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EXAMPLE
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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
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CROSSREFS
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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
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin Dec 05 2011
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STATUS
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approved
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