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A219708 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 nonincreasing columns, 0..3 n X 2 array. 1
4, 13, 44, 129, 338, 813, 1822, 3840, 7665, 14578, 26557, 46556, 78861, 129536, 206973, 322561, 491490, 733707, 1075042, 1548523, 2195900, 3069399, 4233728, 5768358, 7770103, 10356024, 13666683, 17869774, 23164159, 29784338, 38005383 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 2 of A219714.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = (1/40320)*n^8 + (1/2016)*n^7 + (7/2880)*n^6 + (5/144)*n^5 + (167/5760)*n^4 + (259/288)*n^3 + (4723/10080)*n^2 - (73/168)*n + 3.

Conjectures from Colin Barker, Jul 27 2018: (Start)

G.f.: x*(4 - 23*x + 71*x^2 - 135*x^3 + 173*x^4 - 147*x^5 + 79*x^6 - 24*x^7 + 3*x^8) / (1 - x)^9.

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.

(End)

EXAMPLE

Some solutions for n=3:

..0..0....0..0....0..0....2..2....0..0....2..2....0..0....1..1....0..0....1..1

..0..3....0..1....0..1....0..0....0..1....2..3....0..1....0..0....0..0....1..2

..3..3....2..3....3..3....0..2....1..3....3..3....0..0....0..3....0..2....1..1

CROSSREFS

Cf. A219714.

Sequence in context: A042767 A286175 A252831 * A345230 A117882 A257674

Adjacent sequences:  A219705 A219706 A219707 * A219709 A219710 A219711

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 26 2012

STATUS

approved

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Last modified July 25 19:34 EDT 2021. Contains 346291 sequences. (Running on oeis4.)