A264565 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having directed index change 1,0 1,1 0,-1 or -1,1.

2, 8, 44, 192, 888, 4104, 18540, 85752, 389340, 1787832, 8158644, 37336464, 170669592, 780379920, 3568245048, 16314092712, 74594729628, 341056001520, 1559406670200, 7129910871000, 32599645712604, 149052729608136

Offset

1,1

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.: 2*x*(1 + 4*x + 4*x^2 - 12*x^3 - 51*x^4 - 72*x^5 - 81*x^6) / ((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:
..1..2..3..7..8....1..5..6..7..8....1..5..6..7..8....1..5..3..7..8
..0.10.11..9..4....0.10..2..3..4....0.10..2..3..4....6..0..2.12..4
..5..6.13.14.18...11.15.13.17..9...11.12.13.17..9...11.15.16.14..9
.16.20.12.22.23...16.20.12.19.14...16.20.18.22.14...10.20.18.13.23
.21.15.17.24.19...21.22.23.24.18...21.15.23.24.19...21.22.17.24.19

Crossrefs

Column 4 of A264569.

Sequence in context: A334335 A283416 A075817 * A018985 A018986 A192469

Adjacent sequences: A264562 A264563 A264564 * A264566 A264567 A264568

Keyword

nonn

Author

R. H. Hardin, Nov 17 2015

Status

approved