A264472 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having directed index change 0,1 1,0 2,1 or -1,-1.

0, 8, 16, 120, 456, 2232, 10116, 45792, 212112, 960336, 4418388, 20134008, 92208780, 421315344, 1926779076, 8809428456, 40277366640, 184164908040, 842016117672, 3849965354232, 17602701446772, 80483933441520, 367989633268848

Offset

1,2

Links

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

Formula

Empirical: a(n) = 18*a(n-2) + 36*a(n-3) - 45*a(n-4) - 216*a(n-5) - 243*a(n-6) for n>7.

Empirical g.f.: 4*x^2*(2 + 4*x - 6*x^2 - 30*x^3 - 36*x^4 + 9*x^5) / ((1 - 3*x^2 - 9*x^3)*(1 - 15*x^2 - 27*x^3)). - Colin Barker, Jan 08 2019

Example

Some solutions for n=4:
..6..0..8..9..3....6..7..1..2..3....6..7..8..2..3....6..7..1..2..3
.11..5..2..7..4....0..5.13.14..4....0..1.13.14..4....0..5.13.14..4
.16.10..1.12.13...16.10.11.12..9...16.17.11.19..9...16.10.11.19..9
.21.22.23.24.14...21.22.23.24..8...10..5.12.24.18...21.22.12.24..8
.15.20.17.18.19...15.20.17.18.19...15.20.21.22.23...15.20.17.18.23

Crossrefs

Column 4 of A264476.

Sequence in context: A230930 A080452 A270377 * A264478 A277364 A278312

Adjacent sequences: A264469 A264470 A264471 * A264473 A264474 A264475

Keyword

nonn

Author

R. H. Hardin, Nov 14 2015

Status

approved