A229448 Number of 5 X n 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

17, 47, 128, 324, 753, 1609, 3184, 5890, 10281, 17075, 27176, 41696, 61977, 89613, 126472, 174718, 236833, 315639, 414320, 536444, 685985, 867345, 1085376, 1345402, 1653241, 2015227, 2438232, 2929688, 3497609, 4150613, 4897944, 5749494, 6715825

Offset

1,1

Links

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

Formula

Empirical: a(n) = (11/60)*n^5 - (1/2)*n^4 + (15/4)*n^3 - 1*n^2 + (257/30)*n + 6.

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

G.f.: x*(17 - 55*x + 101*x^2 - 79*x^3 + 44*x^4 - 6*x^5) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Example

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

Crossrefs

Row 5 of A229445.

Sequence in context: A201792 A039949 A220081 * A155841 A147058 A083296

Adjacent sequences: A229445 A229446 A229447 * A229449 A229450 A229451

Keyword

nonn

Author

R. H. Hardin, Sep 23 2013

Status

approved