A220011 Number of 2 X n 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 nonincreasing columns, 0..3 2 X n array.

4, 7, 19, 43, 85, 154, 263, 431, 685, 1062, 1611, 2395, 3493, 5002, 7039, 9743, 13277, 17830, 23619, 30891, 39925, 51034, 64567, 80911, 100493, 123782, 151291, 183579, 221253, 264970, 315439, 373423, 439741, 515270, 600947, 697771, 806805, 929178

Offset

1,1

Comments

Row 2 of A220010.

Links

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

Formula

Empirical: a(n) = (1/60)*n^5 - (1/4)*n^4 + (31/12)*n^3 - (35/4)*n^2 + (102/5)*n - 17 for n>2.

Conjectures from Colin Barker, Jul 29 2018: (Start)

G.f.: x*(4 - 17*x + 37*x^2 - 46*x^3 + 32*x^4 - 10*x^5 + x^6 + x^7) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>8.

(End)

Example

Some solutions for n=3:
  3 1 1    1 1 0    2 1 1    3 0 0    3 3 3    2 2 0    3 2 2
  3 1 1    1 0 0    1 1 1    3 0 0    3 3 3    2 0 0    3 2 2

Crossrefs

Cf. A220010.

Sequence in context: A352007 A182646 A190646 * A305034 A133264 A253208

Adjacent sequences: A220008 A220009 A220010 * A220012 A220013 A220014

Keyword

nonn

Author

R. H. Hardin, Dec 03 2012

Status

approved