A220034 Number of 4 X n 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 4 X n array.

5, 8, 15, 34, 61, 95, 137, 187, 246, 315, 395, 487, 592, 711, 845, 995, 1162, 1347, 1551, 1775, 2020, 2287, 2577, 2891, 3230, 3595, 3987, 4407, 4856, 5335, 5845, 6387, 6962, 7571, 8215, 8895, 9612, 10367, 11161, 11995, 12870, 13787, 14747, 15751, 16800

Offset

1,1

Comments

Row 4 of A220032.

Links

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

Formula

Empirical: a(n) = (1/6)*n^3 + (1/2)*n^2 + (43/3)*n - 45 for n>5.

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

G.f.: x*(5 - 12*x + 13*x^2 + 2*x^3 - 12*x^4 + 3*x^5 + 2*x^6 - x^7 + x^8) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>9.

(End)

Example

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

Crossrefs

Cf. A220032.

Sequence in context: A327605 A259724 A259585 * A063731 A129316 A039752

Adjacent sequences: A220031 A220032 A220033 * A220035 A220036 A220037

Keyword

nonn

Author

R. H. Hardin, Dec 03 2012

Status

approved