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A202511
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T(n,k)=Number of zero-sum -k..k arrays of n elements with first through third differences also in -k..k.
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12
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1, 1, 1, 1, 3, 3, 1, 3, 5, 1, 1, 5, 15, 15, 5, 1, 5, 21, 29, 21, 9, 1, 7, 27, 75, 95, 53, 7, 1, 7, 47, 115, 239, 255, 109, 11, 1, 9, 57, 217, 529, 883, 747, 239, 13, 1, 9, 67, 297, 1041, 2369, 3285, 2215, 489, 13, 1, 11, 97, 479, 1785, 5429, 10799, 12619, 6649, 1051, 23, 1, 11
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OFFSET
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1,5
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LINKS
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EXAMPLE
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Table starts
..1....1.....1......1.......1.......1........1........1.........1.........1
..1....3.....3......5.......5.......7........7........9.........9........11
..3....5....15.....21......27......47.......57.......67........97.......111
..1...15....29.....75.....115.....217......297......479.......609.......887
..5...21....95....239.....529....1041.....1785.....3009......4655......6937
..9...53...255....883....2369....5429....11015....20519.....35743.....58863
..7..109...747...3285...10799...29295....68781...145389....282771....514931
.11..239..2215..12619...50519..161469...436919..1046251...2272569...4571935
.13..489..6649..48079..235731..890659..2782455..7550637..18334273..40766453
.13.1051.19967.185533.1110857.4953959.17852623.54870161.148884915.365789931
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Some solutions for n=8 k=7
.-1...-2...-5...-4...-6...-6...-1...-2...-4...-4...-3...-5...-3...-4...-1...-3
.-4...-4...-4...-3...-6...-4...-5...-5...-3...-5...-6...-4...-1...-3...-3...-1
.-2...-5...-1....0...-5...-3...-3...-1...-1...-2...-4...-2...-2...-1...-2....4
.-2...-5....3....4....1....0...-1....3...-1....3...-1....2...-3...-1....1....5
..2....1....3....7....5....3....4....3...-3....6....3....3....1....3....2....1
..5....6....2....4....5....6....6....1....0....3....5....3....4....4....1...-2
..4....5....0...-1....5....3....2...-1....5...-1....6....4....5....2...-1...-2
.-2....4....2...-7....1....1...-2....2....7....0....0...-1...-1....0....3...-2
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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