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 A219465 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 n X 2 array. 1

%I #8 Jul 26 2018 05:17:14

%S 4,23,82,239,619,1471,3259,6800,13464,25453,46178,80755,136643,224449,

%T 358927,560200,855236,1279611,1879594,2714591,3859987,5410427,7483579,

%U 10224424,13810120,18455489,24419178,32010547,41597339,53614189,68572031

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

%C Column 2 of A219471.

%H R. H. Hardin, <a href="/A219465/b219465.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/20160)*n^8 + (1/1260)*n^7 + (1/480)*n^6 + (4/45)*n^5 - (11/960)*n^4 + (277/180)*n^3 + (7607/5040)*n^2 + (61/70)*n.

%F Conjectures from _Colin Barker_, Jul 26 2018: (Start)

%F G.f.: x*(4 - 13*x + 19*x^2 - 7*x^3 - 8*x^4 + 10*x^5 - 2*x^6 - x^7) / (1 - x)^9.

%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

%F (End)

%e Some solutions for n=3:

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

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

%e ..0..1....3..3....0..3....0..0....0..3....1..3....1..2....0..0....3..3....2..3

%Y Cf. A219471.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 20 2012

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Last modified September 17 19:20 EDT 2024. Contains 375990 sequences. (Running on oeis4.)