A219350 Number of n X 4 arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..1 n X 4 array.

4, 4, 15, 35, 81, 174, 364, 740, 1459, 2778, 5105, 9069, 15615, 26129, 42600, 67827, 105680, 161425, 242124, 357122, 518634, 742446, 1048745, 1463094, 2017569, 2752076, 3715867, 4969275, 6585689, 8653791, 11280078, 14591693, 18739590

Offset

1,1

Comments

Column 4 of A219354.

Links

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

Formula

Empirical: a(n) = (1/40320)*n^8 - (1/1120)*n^7 + (5/192)*n^6 - (2/5)*n^5 + (7429/1920)*n^4 - (3037/160)*n^3 + (34483/2016)*n^2 + (71507/280)*n - 791 for n>7.

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

G.f.: x*(4 - 32*x + 123*x^2 - 292*x^3 + 474*x^4 - 555*x^5 + 496*x^6 - 364*x^7 + 235*x^8 - 139*x^9 + 82*x^10 - 48*x^11 + 22*x^12 - 7*x^13 + 3*x^14 - x^15) / (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>16.

(End)

Example

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

Crossrefs

Cf. A219354.

Sequence in context: A048282 A068592 A198313 * A222511 A135944 A268169

Adjacent sequences: A219347 A219348 A219349 * A219351 A219352 A219353

Keyword

nonn

Author

R. H. Hardin, Nov 18 2012

Status

approved