The On-Line Encyclopedia of Integer Sequences (OEIS)

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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 or two consecutive decreases.
(history; published version)

#4 by R. H. Hardin at Fri Oct 23 11:22:59 EDT 2015

STATUS

editing

approved

#3 by R. H. Hardin at Fri Oct 23 11:22:55 EDT 2015

LINKS

R. H. Hardin, <a href="/A263666/b263666.txt">Table of n, a(n) for n = 1..484</a>

#2 by R. H. Hardin at Fri Oct 23 11:22:40 EDT 2015

NAME

allocated for R. H. Hardin

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.

DATA

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

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.

KEYWORD

allocated

nonn,tabl

AUTHOR

R. H. Hardin, Oct 23 2015

STATUS

approved

editing

#1 by R. H. Hardin at Fri Oct 23 11:14:54 EDT 2015

NAME

allocated for R. H. Hardin

KEYWORD

allocated

STATUS

approved