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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.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Apr 25 2012
STATUS
approved