A264484 Number of (n+1) X (1+1) arrays of permutations of 0..n*2+1 with each element having directed index change 2,-1 1,0 2,1 0,-1 -2,-2 or -1,0.

1, 3, 4, 12, 25, 52, 121, 261, 576, 1280, 2809, 6204, 13689, 30167, 66564, 146804, 323761, 714136, 1575025, 3473817, 7661824, 16898560, 37271025, 82203912, 181306225, 399883707, 881971204, 1945248444, 4290381001, 9462732780

Offset

1,2

Links

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

Formula

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

Empirical g.f.: x*(1 + x - 2*x^2 + 3*x^3 - x^7) / ((1 - 2*x - x^3)*(1 + 2*x^4 - x^6)). - Colin Barker, Jan 08 2019

Example

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

Crossrefs

Column 1 of A264490.

Sequence in context: A000577 A333163 A111758 * A343163 A000942 A255436

Adjacent sequences: A264481 A264482 A264483 * A264485 A264486 A264487

Keyword

nonn

Author

R. H. Hardin, Nov 14 2015

Status

approved