A264054 Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having index change +-(.,.) 0,0 1,2 or 2,-2.

2, 8, 18, 45, 125, 320, 832, 2197, 5733, 14994, 39304, 102850, 269225, 704969, 1845504, 4831488, 12649337, 33116057, 86698690, 226981000, 594243090, 1555747893, 4073003173, 10663258432, 27916771136, 73087061741, 191344405725

Offset

1,1

Comments

Column 2 of A264059.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 3*a(n-1) - a(n-2) + 3*a(n-3) - 9*a(n-4) + 3*a(n-5) - a(n-6) + 3*a(n-7) - a(n-8).

Empirical g.f.: x*(2 + 2*x - 4*x^2 - 7*x^3 + 2*x^4 + 2*x^5 + 2*x^6 - x^7) / ((1 - 3*x + x^2)*(1 - 3*x^3 + x^6)). - Colin Barker, Mar 20 2018

Example

Some solutions for n=4:
..5..1..6....5..1..6....0..1..6....0..1..6....5..1..2....0..1..2....5..1..6
..3..4..0....3..4..0....8..4..5....3..4..5....8..4..0....8..4..9....3..4..0
..2..7..8....2..7.12....2..7..3....2..7.12...11..7..3...11..7..3....2..7.12
.14.10.11...14.10.11....9.10.11....9.10.11....9.10..6....5.10..6....9.10.11
.12.13..9....8.13..9...12.13.14....8.13.14...12.13.14...12.13.14....8.13.14

Crossrefs

Cf. A264059.

Sequence in context: A058858 A236633 A212518 * A073307 A064009 A246148

Adjacent sequences: A264051 A264052 A264053 * A264055 A264056 A264057

Keyword

nonn

Author

R. H. Hardin, Nov 02 2015

Status

approved