A264251 Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having directed index change 0,1 0,-1 0,2 1,0 or -1,0.

10, 33, 180, 760, 3653, 16401, 76330, 348480, 1607429, 7373520, 33925033, 155833327, 716445000, 3292287537, 15133013897, 69549148120, 319662372941, 1469173559040, 6752499229970, 31034919432791, 142639437485117

Offset

1,1

Links

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

Formula

Empirical: a(n) = a(n-1) + 16*a(n-2) + 9*a(n-3) - 29*a(n-4) - 9*a(n-5) + 16*a(n-6) - a(n-7) - a(n-8).

Empirical g.f.: x*(1 - x)*(10 + 33*x + 20*x^2 - 18*x^3 - 12*x^4 + 3*x^5 + x^6) / (1 - x - 16*x^2 - 9*x^3 + 29*x^4 + 9*x^5 - 16*x^6 + x^7 + x^8). - Colin Barker, Jan 06 2019

Example

Some solutions for n=4:
..3..2..5....3..4..5....1..2..0....3..2..5....1..0..5....1..2..0....1..0..5
..0..1..4....0..1..2....6..3..4....0..1..4....6..3..2....6..5..4....4..3..2
..9..8..6....9.10..7....7..8..5....7.10.11....7..4.11....3..8.11....7..8..6
.12..7.14....6.11..8...12.11.14....6..9..8...10..9..8...12..7.14...12..9.14
.13.10.11...13.14.12....9.10.13...13.14.12...13.14.12....9.10.13...13.10.11

Crossrefs

Column 2 of A264257.

Sequence in context: A211033 A020479 A219818 * A140866 A219848 A320565

Adjacent sequences: A264248 A264249 A264250 * A264252 A264253 A264254

Keyword

nonn

Author

R. H. Hardin, Nov 09 2015

Status

approved