A264332 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having directed index change -1,1 1,0 1,-1 or 0,-1.

1, 8, 40, 240, 1528, 8976, 51904, 302328, 1757848, 10199400, 59182576, 343432200, 1992680992, 11561675184, 67081902808, 389213984040, 2258240299432, 13102425739632, 76020937882840, 441077255457840, 2559151966018144

Offset

1,2

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 5*a(n-2) + 36*a(n-3) - 72*a(n-4) - 243*a(n-6) for n>7.

Empirical g.f.: x*(1 + 2*x - 3*x^2 + 4*x^3 + 72*x^4 + 144*x^5 + 171*x^6) / ((1 - x - 9*x^3)*(1 - 5*x - 27*x^3)). - Colin Barker, Jan 07 2019

Example

Some solutions for n=4:
..1..5..6..7..8....1..2..6..7..8....1..5..6..7..8....1..5..3..7..8
..0..2..3.12..4....0.10..3..4.13....0..2..3.12..4....0.10..2..4.13
.11.15.16.14..9....5.15.16.14..9...11.15.16.14..9....6.12.16..9.18
.10.20.13.22.23...11.20.12.22.23...10.20.18.13.23...11.20.21.22.14
.21.17.18.24.19...21.17.18.24.19...21.22.17.24.19...15.17.23.24.19

Crossrefs

Column 4 of A264336.

Sequence in context: A068775 A068774 A073955 * A188332 A158922 A117083

Adjacent sequences: A264329 A264330 A264331 * A264333 A264334 A264335

Keyword

nonn

Author

R. H. Hardin, Nov 11 2015

Status

approved