A211924 Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any horizontal, vertical or antidiagonal neighbor, and containing the value n(n+1)/2-2

0, 2, 9, 31, 80, 171, 322, 554, 891, 1360, 1991, 2817, 3874, 5201, 6840, 8836, 11237, 14094, 17461, 21395, 25956, 31207, 37214, 44046, 51775, 60476, 70227, 81109, 93206, 106605, 121396, 137672, 155529, 175066, 196385, 219591, 244792, 272099, 301626

Offset

1,2

Comments

Column 1 of A211930.

Links

R. H. Hardin, Table of n, a(n) for n = 1..74

Formula

Empirical: a(n) = (1/8)*n^4 + (1/4)*n^3 - (13/8)*n^2 + (9/4)*n for n>1.

Conjectures from Colin Barker, Mar 09 2018: (Start)

G.f.: x^2*(2 - x)*(1 + 3*x^2 - x^3) / (1 - x)^5.

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........0........0........0........0........0........0
..1.2......1.2......1.0......1.2......1.2......1.2......1.2......1.2
..3.4.5....3.4.5....2.3.4....3.0.4....3.4.5....0.3.4....3.4.5....3.4.3
..6.0.7.8..6.2.7.8..5.6.7.8..5.6.7.8..6.7.8.4..5.6.7.8..6.7.8.7..5.6.7.8

Crossrefs

Cf. A211930.

Sequence in context: A084652 A188776 A261443 * A295134 A277242 A277243

Adjacent sequences: A211921 A211922 A211923 * A211925 A211926 A211927

Keyword

nonn

Author

R. H. Hardin, Apr 25 2012

Status

approved