A264365 Number of (1+1) X (n+1) arrays of permutations of 0..n*2+1 with each element having directed index change 0,0 0,2 1,0 or -1,-2.

1, 3, 9, 18, 36, 78, 169, 364, 784, 1680, 3600, 7740, 16641, 35733, 76729, 164815, 354025, 760410, 1633284, 3508110, 7535025, 16184520, 34762816, 74666944, 160376896, 344473464, 739894401, 1589218425, 3413480625, 7331811675

Offset

1,2

Links

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

Formula

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

Empirical g.f.: x*(1 + 2*x + 6*x^2 + 6*x^3 + 6*x^4 + 3*x^5 - 2*x^6 - 3*x^7 - x^8) / ((1 + x^2 - x^3)*(1 + x^2 + x^3)*(1 - x - 2*x^2 - x^3)). - Colin Barker, Jan 07 2019

Example

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

Crossrefs

Row 1 of A264364.

Sequence in context: A000241 A028723 A213291 * A291143 A057578 A271370

Adjacent sequences: A264362 A264363 A264364 * A264366 A264367 A264368

Keyword

nonn

Author

R. H. Hardin, Nov 12 2015

Status

approved