A220030 Number of n X 6 arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 n X 6 array.

6, 15, 42, 95, 192, 358, 626, 1038, 1646, 2513, 3714, 5337, 7484, 10272, 13834, 18320, 23898, 30755, 39098, 49155, 61176, 75434, 92226, 111874, 134726, 161157, 191570, 226397, 266100, 311172, 362138, 419556, 484018, 556151, 636618, 726119, 825392

Offset

1,1

Comments

Column 6 of A220032.

Links

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

Formula

Empirical: a(n) = (1/120)*n^5 + (1/8)*n^4 + (5/24)*n^3 + (15/8)*n^2 + (227/60)*n - 4 for n>1.

Conjectures from Colin Barker, Jul 30 2018: (Start)

G.f.: x*(3 - 6*x + 6*x^2 - 2*x^3)*(2 - 3*x + 4*x^2 - 2*x^3) / (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>7.

(End)

Example

Some solutions for n=3.
..1..1..0..0..0..0....0..0..0..0..0..0....1..0..0..0..0..0....0..0..0..0..0..0
..1..1..0..0..0..0....1..0..0..0..0..0....1..0..0..0..0..0....0..0..0..0..0..0
..1..1..1..1..0..0....1..0..0..0..0..0....1..0..0..0..0..0....1..1..0..0..0..0

Crossrefs

Cf. A220032.

Sequence in context: A114696 A106368 A100491 * A230165 A271687 A271809

Adjacent sequences: A220027 A220028 A220029 * A220031 A220032 A220033

Keyword

nonn

Author

R. H. Hardin, Dec 03 2012

Status

approved