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A263666
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 or two consecutive decreases.
7
1, 1, 2, 1, 2, 2, 1, 2, 4, 2, 1, 2, 4, 7, 2, 1, 2, 4, 10, 8, 2, 1, 2, 4, 10, 22, 12, 2, 1, 2, 4, 10, 32, 40, 16, 2, 1, 2, 4, 10, 32, 95, 70, 24, 2, 1, 2, 4, 10, 32, 122, 208, 133, 32, 2, 1, 2, 4, 10, 32, 122, 422, 486, 254, 48, 2, 1, 2, 4, 10, 32, 122, 544, 1222, 1064, 482, 64, 2, 1, 2, 4, 10, 32
OFFSET
1,3
COMMENTS
Table starts
.1..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
.2..4...4....4....4.....4.....4.....4......4......4......4......4......4......4
.2..7..10...10...10....10....10....10.....10.....10.....10.....10.....10.....10
.2..8..22...32...32....32....32....32.....32.....32.....32.....32.....32.....32
.2.12..40...95..122...122...122...122....122....122....122....122....122....122
.2.16..70..208..422...544...544...544....544....544....544....544....544....544
.2.24.133..486.1222..2287..2770..2770...2770...2770...2770...2770...2770...2770
.2.32.254.1064.3302..7688.13102.15872..15872..15872..15872..15872..15872..15872
.2.48.482.2560.9021.25662.53324.86555.101042.101042.101042.101042.101042.101042
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) for n>2
k=2: a(n) = 2*a(n-2) for n>6
k=3: a(n) = 3*a(n-2) +2*a(n-4) for n>12
k=4: a(n) = 4*a(n-2) +6*a(n-4) +16*a(n-6) -8*a(n-10) for n>20
k=5: [order 22] for n>34
k=6: [order 52] for n>66
EXAMPLE
Some solutions for n=7 k=4
..1....1....1....0....1....2....2....2....4....3....1....1....3....4....1....4
..0....0....5....3....5....1....0....3....0....1....5....0....4....0....4....0
..6....6....3....1....4....5....6....0....6....4....0....5....1....3....2....5
..4....2....4....5....6....0....1....6....2....0....6....4....6....2....6....1
..5....5....0....2....0....6....4....1....5....6....3....6....0....5....0....6
..2....3....6....6....3....3....3....5....1....2....4....2....5....1....5....2
..3....4....2....4....2....4....5....4....3....5....2....3....2....6....3....3
CROSSREFS
Diagonal is A001250.
Sequence in context: A350700 A178522 A131240 * A107027 A355395 A107030
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Oct 23 2015
STATUS
approved