A264004 Number of (1+1) X (n+1) arrays of permutations of 0..n*2+1 with each element having index change (+-,+-) 0,0 1,2 or 1,0.

4, 18, 81, 288, 1024, 3872, 14641, 54450, 202500, 756450, 2825761, 10543232, 39337984, 146821248, 547981281, 2045057058, 7632119044, 28483593842, 106302733681, 396726688800, 1480602240000, 5525684704800, 20622143227921

Offset

1,1

Comments

Row 1 of A264003.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 4*a(n-2) + 12*a(n-3) - 12*a(n-5) + 4*a(n-6) - 4*a(n-7) + a(n-8).

Empirical g.f.: x*(4 + 2*x + 25*x^2 - 12*x^3 - 20*x^4 + 4*x^5 - 7*x^6 + 2*x^7) / ((1 - x)*(1 + x)*(1 - 4*x + x^2)*(1 + 4*x^2 + x^4)). - Colin Barker, Mar 20 2018

Example

Some solutions for n=4:
..0..1..7..3..9....0..8..7..6..4....0..6..9..8..7....0..6..9..8..7
..5..6..4..8..2....5..3..2..1..9....5..3..2..1..4....5..1..4..3..2

Crossrefs

Cf. A264003.

Sequence in context: A104631 A106391 A063881 * A282708 A252823 A264191

Adjacent sequences: A264001 A264002 A264003 * A264005 A264006 A264007

Keyword

nonn

Author

R. H. Hardin, Oct 31 2015

Status

approved