A211958 Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any diagonal or antidiagonal neighbor, and containing the value n(n+1)/2-2.

0, 3, 12, 37, 90, 186, 343, 582, 927, 1405, 2046, 2883, 3952, 5292, 6945, 8956, 11373, 14247, 17632, 21585, 26166, 31438, 37467, 44322, 52075, 60801, 70578, 81487, 93612, 107040, 121861, 138168, 156057, 175627, 196980, 220221, 245458, 272802, 302367

Offset

1,2

Comments

Column 1 of A211963.

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 - (9/8)*n^2 + (7/4)*n for n>1.

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

G.f.: x^2*(3 - 3*x + 7*x^2 - 5*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......1.1......1.2......1.2......1.2
..3.4.5....3.0.4....3.4.5....3.4.5....2.3.4....1.3.4....3.4.0....3.4.5
..3.6.7.8..5.6.7.8..6.7.8.0..6.0.7.8..5.6.7.8..5.6.7.8..5.6.7.8..6.7.8.1

Crossrefs

Cf. A211963.

Sequence in context: A102744 A145951 A083215 * A255610 A022727 A290930

Adjacent sequences: A211955 A211956 A211957 * A211959 A211960 A211961

Keyword

nonn

Author

R. H. Hardin, Apr 26 2012

Status

approved