A264122 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,-1.

2, 9, 45, 200, 845, 3549, 14994, 63525, 269225, 1140624, 4831721, 20466953, 86698690, 367261713, 1555747893, 6590256856, 27916775317, 118257348165, 500946152850, 2122041959565, 8989114033297, 38078498156832, 161303106660625

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) + a(n-2) - 4*a(n-3) + 16*a(n-4) + 4*a(n-5) + a(n-6) - 4*a(n-7) - a(n-8).

Empirical g.f.: x*(2 + x + 7*x^2 + 19*x^3 + 4*x^4 - 3*x^5 - 5*x^6 - x^7) / ((1 + x - x^2)*(1 - 4*x - x^2)*(1 - x + 2*x^2 + x^3 + x^4)). - Colin Barker, Jan 04 2019

Example

Some solutions for n=4:
..0..6..3....0..6..7....0..1..2....0..6..2....0..1..2....0..6..2....0..6..3
..2..9..5....3..9..5....3..4..6....3..9.10....3..4..6....3..4..5....2..9.10
..1..7..8....1..2..8....5..7.13....1..7..8....5.12.13....1.12.13....1..7..8
..4.10.12....4.10.12....9.10.12....4..5.12....9.10.11....9.10.11....4..5.11
.11.13.14...11.13.14...11..8.14...11.13.14....7..8.14....7..8.14...12.13.14

Crossrefs

Column 2 of A264128.

Sequence in context: A059392 A264111 A370089 * A233505 A228767 A074607

Adjacent sequences: A264119 A264120 A264121 * A264123 A264124 A264125

Keyword

nonn

Author

R. H. Hardin, Nov 03 2015

Status

approved