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A219349
Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..1 n X 3 array.
1
3, 3, 8, 15, 27, 46, 76, 122, 190, 287, 421, 601, 837, 1140, 1522, 1996, 2576, 3277, 4115, 5107, 6271, 7626, 9192, 10990, 13042, 15371, 18001, 20957, 24265, 27952, 32046, 36576, 41572, 47065, 53087, 59671, 66851, 74662, 83140, 92322, 102246, 112951
OFFSET
1,1
COMMENTS
Column 3 of A219354.
LINKS
FORMULA
Empirical: a(n) = (1/24)*n^4 - (1/4)*n^3 + (23/24)*n^2 + (13/4)*n - 8 for n > 3.
Conjectures from Colin Barker, Jul 25 2018: (Start)
G.f.: x*(3 - 12*x + 23*x^2 - 25*x^3 + 17*x^4 - 7*x^5 + 3*x^6 - x^7) / (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 > 8.
(End)
EXAMPLE
Some solutions for n=3:
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1
0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 1
CROSSREFS
Cf. A219354.
Sequence in context: A126592 A055057 A154029 * A208964 A104864 A300367
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 18 2012
STATUS
approved