A212039 Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any element within a city block distance of two, and containing the value n(n+1)/2-2.

0, 1, 4, 19, 58, 136, 271, 484, 799, 1243, 1846, 2641, 3664, 4954, 6553, 8506, 10861, 13669, 16984, 20863, 25366, 30556, 36499, 43264, 50923, 59551, 69226, 80029, 92044, 105358, 120061, 136246, 154009, 173449, 194668, 217771, 242866, 270064, 299479

Offset

1,3

Comments

Column 1 of A212044.

Links

R. H. Hardin, Table of n, a(n) for n = 1..73

Formula

Empirical: a(n) = (1/8)*n^4 + (1/4)*n^3 - (25/8)*n^2 + (23/4)*n - 2 for n>1.

Conjectures from Colin Barker, Jul 20 2018: (Start)

G.f.: x^2*(1 - x + 9*x^2 - 7*x^3 + x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>6.

(End)

Example

Some solutions for n=4:
..0........0........0........0........0........0........0........0
..1.2......1.2......1.2......1.2......1.2......1.2......1.2......1.2
..3.4.5....3.4.5....3.4.5....3.4.5....3.4.1....3.4.5....3.4.5....3.4.5
..6.7.8.1..6.7.8.0..6.7.3.8..6.7.0.8..5.6.7.8..6.7.8.3..6.7.2.8..6.1.7.8

Crossrefs

Cf. A212044.

Sequence in context: A332697 A134507 A098813 * A055485 A000306 A100185

Adjacent sequences: A212036 A212037 A212038 * A212040 A212041 A212042

Keyword

nonn

Author

R. H. Hardin, Apr 28 2012

Status

approved