A219515 Number of n X 4 arrays of the minimum value of corresponding elements and their horizontal, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..1 n X 4 array.

4, 5, 24, 68, 187, 465, 1090, 2430, 5181, 10575, 20714, 39046, 71023, 124990, 213360, 354136, 572847, 904971, 1398924, 2119700, 3153253, 4611718, 6639574, 9420858, 13187545, 18229215, 24904134, 33651882, 45007667, 59618470, 78261172

Offset

1,1

Comments

Column 4 of A219519.

Links

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

Formula

Empirical: a(n) = (1/6720)*n^8 - (1/360)*n^7 + (41/1440)*n^6 + (7/18)*n^5 - (41099/2880)*n^4 + (68651/360)*n^3 - (6724661/5040)*n^2 + (58709/12)*n - 7380 for n>6.

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

G.f.: x*(4 - 31*x + 123*x^2 - 304*x^3 + 523*x^4 - 660*x^5 + 655*x^6 - 528*x^7 + 357*x^8 - 217*x^9 + 156*x^10 - 128*x^11 + 74*x^12 - 15*x^13 - 3*x^14) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>15.

(End)

Example

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

Crossrefs

Cf. A219519.

Sequence in context: A089499 A249060 A042601 * A248246 A164054 A333321

Adjacent sequences: A219512 A219513 A219514 * A219516 A219517 A219518

Keyword

nonn

Author

R. H. Hardin, Nov 21 2012

Status

approved