A264677 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having directed index change -1,-1 1,0 -1,-2 -2,-2 or 0,1.

1, 2, 10, 29, 75, 201, 588, 1700, 4785, 13401, 37905, 107598, 304638, 860789, 2433555, 6885713, 19483112, 55110392, 155875521, 440924465, 1247301569, 3528321578, 9980556450, 28232081677, 79861067099, 225905953689, 639026458132

Offset

1,2

Links

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

Formula

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

Empirical g.f.: x*(1 - x + 7*x^2 + x^4 + 4*x^5 - 2*x^6 - x^8) / (1 - 3*x + 3*x^2 - 5*x^3 - 7*x^4 + 5*x^5 - 7*x^6 + 3*x^7 - x^8 + x^9). - Colin Barker, Jan 08 2019

Example

Some solutions for n=4:
.12..7..9..2..3....6..7..1..2..3....6.13..8..2..3...12..0..1..2..3
..0..1..6.14..4....0.12.13.14..4....0..1.14..7..4...11.13..6.14..4
..5.10.11..8.13....5.10.11..8..9....5.10.11.12..9....5.10..7..8..9

Crossrefs

Row 2 of A264676.

Sequence in context: A203551 A344791 A192976 * A101561 A279263 A295525

Adjacent sequences: A264674 A264675 A264676 * A264678 A264679 A264680

Keyword

nonn

Author

R. H. Hardin, Nov 20 2015

Status

approved