A219293 Number of n X 2 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 columns, 0..2 n X 2 array.

3, 7, 17, 35, 62, 103, 165, 257, 390, 577, 833, 1175, 1622, 2195, 2917, 3813, 4910, 6237, 7825, 9707, 11918, 14495, 17477, 20905, 24822, 29273, 34305, 39967, 46310, 53387, 61253, 69965, 79582, 90165, 101777, 114483, 128350, 143447, 159845, 177617

Offset

1,1

Comments

Column 2 of A219299.

Links

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

Formula

Empirical: a(n) = (1/12)*n^4 - (2/3)*n^3 + (53/12)*n^2 - (17/6)*n - 3 for n > 2.

Conjectures from Colin Barker, Jul 25 2018: (Start)

G.f.: x*(3 - 8*x + 12*x^2 - 10*x^3 + 2*x^4 + 5*x^5 - 2*x^6) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 7.

(End)

Example

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

Crossrefs

Cf. A219299.

Sequence in context: A168582 A192958 A351405 * A178521 A034482 A114100

Adjacent sequences: A219290 A219291 A219292 * A219294 A219295 A219296

Keyword

nonn

Author

R. H. Hardin, Nov 17 2012

Status

approved