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

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Last modified March 29 01:21 EDT 2023. Contains 361596 sequences. (Running on oeis4.)