A229425 Number of n X 5 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, rows lexicographically nondecreasing, and columns lexicographically nonincreasing.

17, 102, 524, 2204, 7816, 24126, 66503, 166972, 387738, 842802, 1731129, 3385828, 6344979, 11451106, 19987862, 33864276, 55858927, 89938670, 141669058, 218736396, 331604442, 494332150, 725582545, 1049856844, 1498992304

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/259200)*n^10 + (1/6480)*n^9 + (149/60480)*n^8 + (163/7560)*n^7 + (10411/86400)*n^6 + (1063/2160)*n^5 + (19597/12960)*n^4 + (4169/1620)*n^3 + (30649/6300)*n^2 + (215/63)*n + 4.

Conjectures from Colin Barker, Sep 15 2018: (Start)

G.f.: x*(17 - 85*x + 337*x^2 - 755*x^3 + 1172*x^4 - 1284*x^5 + 987*x^6 - 525*x^7 + 186*x^8 - 40*x^9 + 4*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..0....1..0..0..0..0....1..1..0..0..0....2..2..1..1..0
..0..0..0..0..0....1..1..0..0..0....1..1..0..0..0....2..2..1..1..0
..1..1..1..1..0....2..1..1..0..0....2..1..1..1..0....2..2..2..2..1
..2..1..1..1..0....2..2..1..0..0....2..2..1..1..0....2..2..2..2..1

Crossrefs

Column 5 of A229428.

Sequence in context: A234693 A022677 A275919 * A041552 A160767 A078625

Adjacent sequences: A229422 A229423 A229424 * A229426 A229427 A229428

Keyword

nonn

Author

R. H. Hardin, Sep 22 2013

Status

approved