A211899 Number of triangular n X n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any neighbor, and containing the value n(n+1)/2-2.

0, 1, 7, 28, 76, 166, 316, 547, 883, 1351, 1981, 2806, 3862, 5188, 6826, 8821, 11221, 14077, 17443, 21376, 25936, 31186, 37192, 44023, 51751, 60451, 70201, 81082, 93178, 106576, 121366, 137641, 155497, 175033, 196351, 219556, 244756, 272062, 301588

Offset

1,3

Comments

Column 1 of A211904.

Links

R. H. Hardin, Table of n, a(n) for n = 1..75

Formula

Empirical: a(n) = (1/8)*n^4 + (1/4)*n^3 - (13/8)*n^2 + (5/4)*n + 1 for n>1.

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

G.f.: x^2*(1 + 2*x + 3*x^2 - 4*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....3.4.0....2.3.4....3.4.5....3.4.3....3.4.5....0.3.4
..1.6.7.8..6.7.8.7..5.6.7.8..5.6.7.8..4.6.7.8..5.6.7.8..5.6.7.8..5.6.7.8

Crossrefs

Cf. A211904.

Sequence in context: A223765 A064951 A296986 * A073995 A357694 A341986

Adjacent sequences: A211896 A211897 A211898 * A211900 A211901 A211902

Keyword

nonn

Author

R. H. Hardin, Apr 25 2012

Status

approved