A264106 Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having index change +-(.,.) 0,0 0,2 or 1,1.

9, 40, 169, 714, 3025, 12816, 54289, 229970, 974169, 4126648, 17480761, 74049690, 313679521, 1328767776, 5628750625, 23843770274, 101003831721, 427859097160, 1812440220361, 7677619978602, 32522920134769, 137769300517680

Offset

1,1

Comments

Column 2 of A264110.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) + 4*a(n-3) + a(n-4) for n>4.

Empirical: a(n) = round((1/10)*(5+3*sqrt(5))*A000045(3n+3)). - John M. Campbell, Jul 06 2016

Empirical g.f.: x*(9+4*x+9*x^2+2*x^3) / ((1+x^2)*(1-4*x-x^2)). - Colin Barker, Jul 07 2016

Example

Some solutions for n=4:
..4..1..2....4..1..2....4..5..2....0..1..2....0..5..2....0..1..2....0..1..2
..7..0..5....3..0..5....7..0..1....3..4..5....3..8..1....5..8..3....3..8..5
..6..3..8....6..7..8...10..3..8....8.11..6....6.11..4....6.11..4....6.11..4
.13.10.11...11.10..9....9..6.11....9.10..7....9.10..7....9.10..7....9.14..7
.14..9.12...12.13.14...12.13.14...14.13.12...12.13.14...12.13.14...12.13.10

Crossrefs

Cf. A000045, A264110.

Sequence in context: A181960 A219511 A027137 * A026629 A243718 A086349

Adjacent sequences: A264103 A264104 A264105 * A264107 A264108 A264109

Keyword

nonn

Author

R. H. Hardin, Nov 03 2015

Status

approved