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A219293
Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..2 n X 2 array.
1
3, 7, 17, 35, 62, 103, 165, 257, 390, 577, 833, 1175, 1622, 2195, 2917, 3813, 4910, 6237, 7825, 9707, 11918, 14495, 17477, 20905, 24822, 29273, 34305, 39967, 46310, 53387, 61253, 69965, 79582, 90165, 101777, 114483, 128350, 143447, 159845, 177617
OFFSET
1,1
COMMENTS
Column 2 of A219299.
LINKS
FORMULA
Empirical: a(n) = (1/12)*n^4 - (2/3)*n^3 + (53/12)*n^2 - (17/6)*n - 3 for n > 2.
Conjectures from Colin Barker, Jul 25 2018: (Start)
G.f.: x*(3 - 8*x + 12*x^2 - 10*x^3 + 2*x^4 + 5*x^5 - 2*x^6) / (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 > 7.
(End)
EXAMPLE
Some solutions for n=3:
2 2 1 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0
2 2 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0
2 2 0 0 0 0 1 1 1 2 2 2 0 2 1 2 0 0 0 1
CROSSREFS
Cf. A219299.
Sequence in context: A168582 A192958 A351405 * A178521 A034482 A114100
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 17 2012
STATUS
approved