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A219454 Number of n X 2 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..3 n X 2 array. 2

%I

%S 4,4,13,26,57,116,231,450,859,1604,2928,5228,9139,15653,26282,43275,

%T 69900,110803,172457,263715,396482,586522,854417,1226696,1737153,

%U 2428374,3353494,4578206,6183045,8265971,10945276,14362841,18687770,24120429

%N Number of n X 2 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..3 n X 2 array.

%C Column 2 of A219460.

%H R. H. Hardin, <a href="/A219454/b219454.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/40320)*n^8 - (1/2016)*n^7 + (7/2880)*n^6 + (53/720)*n^5 - (6313/5760)*n^4 + (1961/288)*n^3 - (170417/10080)*n^2 + (3393/280)*n + 13 for n>5.

%F Conjectures from _Colin Barker_, Mar 11 2018: (Start)

%F G.f.: x*(4 - 32*x + 121*x^2 - 283*x^3 + 459*x^4 - 553*x^5 + 525*x^6 - 411*x^7 + 271*x^8 - 149*x^9 + 71*x^10 - 29*x^11 + 8*x^12 - x^13) / (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>14.

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Cf. A219460.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 20 2012

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Last modified October 28 04:43 EDT 2021. Contains 348313 sequences. (Running on oeis4.)