A219499 Number of n X 5 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 n X 5 array.

5, 9, 26, 58, 107, 179, 281, 421, 608, 852, 1164, 1556, 2041, 2633, 3347, 4199, 5206, 6386, 7758, 9342, 11159, 13231, 15581, 18233, 21212, 24544, 28256, 32376, 36933, 41957, 47479, 53531, 60146, 67358, 75202, 83714, 92931, 102891, 113633, 125197

Offset

1,1

Comments

Column 5 of A219502.

Links

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

Formula

Empirical: a(n) = (1/24)*n^4 + (1/4)*n^3 + (35/24)*n^2 + (21/4)*n - 13 for n>2.

Conjectures from Colin Barker, Jul 26 2018: (Start)

G.f.: x*(5 - 16*x + 31*x^2 - 32*x^3 + 12*x^4 + 4*x^5 - 3*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:
..1..0..0..0..0....0..0..0..0..0....1..1..1..0..0....0..0..0..0..0
..1..0..0..0..0....1..0..0..0..0....1..1..1..1..0....1..0..0..0..0
..1..1..0..0..0....1..1..1..1..1....1..1..1..1..1....1..1..1..0..0

Crossrefs

Cf. A219502.

Sequence in context: A112084 A038251 A034498 * A048884 A077915 A222357

Adjacent sequences: A219496 A219497 A219498 * A219500 A219501 A219502

Keyword

nonn

Author

R. H. Hardin, Nov 20 2012

Status

approved