A220036 Number of 6 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 6 X n array.

7, 12, 28, 83, 187, 358, 613, 962, 1426, 2034, 2823, 3839, 5137, 6782, 8850, 11429, 14620, 18538, 23313, 29091, 36035, 44326, 54164, 65769, 79382, 95266, 113707, 135015, 159525, 187598, 219622, 256013, 297216, 343706, 395989, 454603, 520119

Offset

1,1

Comments

Row 6 of A220032.

Links

R. H. Hardin, Table of n, a(n) for n = 1..155

Formula

Empirical: a(n) = (1/120)*n^5 - (1/12)*n^4 + (47/24)*n^3 - (23/12)*n^2 + (1771/30)*n - 323 for n>8.

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

G.f.: x*(7 - 30*x + 61*x^2 - 45*x^3 - 26*x^4 + 59*x^5 - 35*x^6 + 3*x^7 + 24*x^8 - 21*x^9 + 3*x^10 + x^11 - x^12 + x^13) / (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>14.

(End)

Example

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

Crossrefs

Cf. A220032.

Sequence in context: A223417 A224699 A078575 * A330589 A197229 A316088

Adjacent sequences: A220033 A220034 A220035 * A220037 A220038 A220039

Keyword

nonn

Author

R. H. Hardin, Dec 03 2012

Status

approved