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 A220148 Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 3 array. 1

%I #7 Jul 30 2018 09:52:44

%S 6,23,77,242,727,2062,5493,13773,32664,73654,158660,327852,652215,

%T 1253089,2331716,4212805,7407330,12701233,21278447,34888718,56073127,

%U 88463032,137171407,209299293,314584340,466223256,681905438,985101192

%N Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 3 array.

%C Column 3 of A220153.

%H R. H. Hardin, <a href="/A220148/b220148.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/19958400)*n^11 + (1/725760)*n^10 + (1/145152)*n^9 + (19/120960)*n^8 + (7/3600)*n^7 + (109/34560)*n^6 + (58081/725760)*n^5 + (26759/181440)*n^4 - (400597/907200)*n^3 + (863/126)*n^2 - (2792/495)*n + 5.

%F Conjectures from _Colin Barker_, Jul 30 2018: (Start)

%F G.f.: x*(6 - 49*x + 197*x^2 - 484*x^3 + 815*x^4 - 997*x^5 + 934*x^6 - 685*x^7 + 389*x^8 - 161*x^9 + 42*x^10 - 5*x^11) / (1 - x)^12.

%F a(n) = 12*a(n-1) - 66*a(n-2) + 220*a(n-3) - 495*a(n-4) + 792*a(n-5) - 924*a(n-6) + 792*a(n-7) - 495*a(n-8) + 220*a(n-9) - 66*a(n-10) + 12*a(n-11) - a(n-12) for n>12.

%F (End)

%e Some solutions for n=3:

%e ..2..0..0....1..1..1....0..0..0....2..0..0....0..0..1....2..1..1....0..0..0

%e ..2..1..1....2..1..1....2..1..0....2..0..0....0..0..0....2..1..1....0..0..0

%e ..2..1..1....2..2..2....2..1..1....2..1..1....1..1..0....2..1..1....2..1..0

%Y Cf. A220153.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 06 2012

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Last modified September 23 21:37 EDT 2023. Contains 365554 sequences. (Running on oeis4.)