A229442 Number of n X 5 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

7, 19, 60, 212, 753, 2546, 8024, 23428, 63430, 159945, 377840, 841419, 1777036, 3578998, 6908102, 12834739, 23041529, 40103959, 67871516, 111976374, 180501843, 284848554, 440842772, 670138334, 1001971536, 1475336877, 2141660944

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/103680)*n^10 + (1/80640)*n^9 + (1/12096)*n^8 + (47/13440)*n^7 + (11/6912)*n^6 + (173/3840)*n^5 + (1187/10368)*n^4 + (12437/20160)*n^3 - (6211/10080)*n^2 + (4901/840)*n + 1.

Conjectures from Colin Barker, Sep 17 2018: (Start)

G.f.: x*(7 - 58*x + 236*x^2 - 558*x^3 + 896*x^4 - 941*x^5 + 709*x^6 - 343*x^7 + 103*x^8 - 17*x^9 + x^10) / (1 - x)^11.

a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.

(End)

Example

Some solutions for n=4:
..0..0..0..0..2....0..2..2..2..2....0..0..2..2..2....0..2..2..2..2
..0..0..0..0..2....1..0..2..2..2....1..1..0..2..2....1..0..2..2..2
..1..1..1..1..0....1..1..0..2..2....1..1..1..0..0....1..1..0..0..0
..1..1..1..1..1....1..1..0..2..2....1..1..1..1..1....1..1..1..1..1

Crossrefs

Column 5 of A229445.

Sequence in context: A263335 A155335 A155226 * A179406 A165683 A092359

Adjacent sequences: A229439 A229440 A229441 * A229443 A229444 A229445

Keyword

nonn

Author

R. H. Hardin, Sep 23 2013

Status

approved