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A263643
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T(n,k)=Number of length n arrays of permutations of 0..n-1 with each element moved by -k to k places and with no two consecutive increases.
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7
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1, 1, 2, 1, 2, 2, 1, 2, 5, 2, 1, 2, 5, 9, 2, 1, 2, 5, 17, 11, 2, 1, 2, 5, 17, 41, 19, 2, 1, 2, 5, 17, 70, 75, 27, 2, 1, 2, 5, 17, 70, 226, 156, 44, 2, 1, 2, 5, 17, 70, 349, 538, 340, 65, 2, 1, 2, 5, 17, 70, 349, 1389, 1417, 738, 104, 2, 1, 2, 5, 17, 70, 349, 2017, 4255, 3734, 1567, 155, 2
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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......1......1......1......1......1
.2...2....2.....2.....2......2......2......2......2......2......2......2......2
.2...5....5.....5.....5......5......5......5......5......5......5......5......5
.2...9...17....17....17.....17.....17.....17.....17.....17.....17.....17.....17
.2..11...41....70....70.....70.....70.....70.....70.....70.....70.....70.....70
.2..19...75...226...349....349....349....349....349....349....349....349....349
.2..27..156...538..1389...2017...2017...2017...2017...2017...2017...2017...2017
.2..44..340..1417..4255...9673..13358..13358..13358..13358..13358..13358..13358
.2..65..738..3734.13529..36321..74678..99377..99377..99377..99377..99377..99377
.2.104.1567.10564.42700.138420.335720.636645.822041.822041.822041.822041.822041
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LINKS
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FORMULA
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Empirical for column k:
k=2: a(n) = 2*a(n-2) +a(n-3) -a(n-5) for n>9
k=3: [order 14] for n>19
k=4: [order 46] for n>53
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EXAMPLE
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Some solutions for n=6 k=4
..2....2....3....0....2....3....3....4....1....4....1....4....4....0....4....1
..0....1....0....5....5....1....4....0....4....5....5....2....3....5....1....0
..4....4....2....1....3....5....2....2....0....2....4....5....5....2....0....4
..1....0....1....3....0....0....5....1....3....0....0....3....0....3....5....3
..5....5....5....2....4....4....0....5....2....3....3....0....2....1....2....5
..3....3....4....4....1....2....1....3....5....1....2....1....1....4....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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