A219916 Number of 3 X n arrays of the minimum value of corresponding elements and their horizontal, diagonal, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 3 X n array.

6, 7, 24, 64, 147, 308, 606, 1144, 2097, 3761, 6628, 11503, 19682, 33216, 55293, 90778, 146960, 234565, 369105, 572645, 876083, 1322052, 1968568, 2893564, 4200467, 6024993, 8543354, 11982091, 16629768, 22850784, 31101583, 41949566, 56095034

Offset

1,1

Comments

Row 3 of A219915.

Links

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

Formula

Empirical: a(n) = (1/362880)*n^9 - (1/10080)*n^8 + (139/60480)*n^7 - (23/720)*n^6 + (5917/17280)*n^5 - (3307/1440)*n^4 + (921359/90720)*n^3 - (391/35)*n^2 - (76861/1260)*n + 182 for n>5.

Conjectures from Colin Barker, Jul 29 2018: (Start)

G.f.: x*(6 - 53*x + 224*x^2 - 581*x^3 + 1007*x^4 - 1204*x^5 + 997*x^6 - 554*x^7 + 179*x^8 + 2*x^9 - 47*x^10 + 43*x^11 - 27*x^12 + 11*x^13 - 2*x^14) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>15.

(End)

Example

Some solutions for n=3:
..1..0..0....1..0..0....1..0..0....1..1..1....2..1..1....1..0..0....1..0..0
..1..0..0....1..0..0....1..0..0....1..1..1....2..1..1....1..0..0....1..0..0
..1..1..1....1..0..0....2..1..1....2..1..1....2..1..1....2..2..2....2..0..0

Crossrefs

Cf. A219915.

Sequence in context: A288771 A067151 A333550 * A135987 A259088 A200179

Adjacent sequences: A219913 A219914 A219915 * A219917 A219918 A219919

Keyword

nonn

Author

R. H. Hardin, Dec 01 2012

Status

approved