A219700 Number of n X 4 arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..1 n X 4 array.

4, 7, 25, 64, 158, 374, 841, 1789, 3619, 7008, 13059, 23510, 41018, 69536, 114803, 184969, 291379, 449542, 680313, 1011318, 1478654, 2128898, 3021461, 4231325, 5852203, 8000164, 10817767, 14478750, 19193322, 25214108, 32842799, 42437561

Offset

1,1

Comments

Column 4 of A219704.

Links

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

Formula

Empirical: a(n) = (1/20160)*n^8 - (1/1680)*n^7 + (1/160)*n^6 + (5/48)*n^5 - (2431/960)*n^4 + (1173/40)*n^3 - (874309/5040)*n^2 + (3728/7)*n - 647 for n>4.

Conjectures from Colin Barker, Jul 27 2018: (Start)

G.f.: x*(4 - 29*x + 106*x^2 - 245*x^3 + 398*x^4 - 466*x^5 + 391*x^6 - 230*x^7 + 106*x^8 - 52*x^9 + 23*x^10 - 2*x^11 - 2*x^12) / (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>13.

(End)

Example

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

Crossrefs

Cf. A219704.

Sequence in context: A129418 A073218 A276288 * A151348 A211942 A110413

Adjacent sequences: A219697 A219698 A219699 * A219701 A219702 A219703

Keyword

nonn

Author

R. H. Hardin, Nov 25 2012

Status

approved