A219769 Number of n X 4 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..1 n X 4 array.

4, 9, 33, 100, 283, 732, 1745, 3881, 8149, 16288, 31169, 57354, 101850, 175100, 292257, 474791, 752483, 1165864, 1769161, 2633816, 3852648, 5544732, 7861073, 10991157, 15170465, 20689040, 27901201, 37236502, 49212038, 64446204, 83674017

Offset

1,1

Comments

Column 4 of A219773.

Links

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

Formula

Empirical: a(n) = (1/10080)*n^8 - (1/120)*n^6 + (73/240)*n^5 - (487/160)*n^4 + (1015/48)*n^3 - (191389/2520)*n^2 + (2351/20)*n - 5 for n>5.

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

G.f.: x*(4 - 27*x + 96*x^2 - 209*x^3 + 319*x^4 - 357*x^5 + 305*x^6 - 190*x^7 + 94*x^8 - 54*x^9 + 35*x^10 - 12*x^11 - x^12 + x^13) / (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>14.

(End)

Example

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

Crossrefs

Cf. A219773.

Sequence in context: A356825 A173659 A054433 * A308038 A096531 A149121

Adjacent sequences: A219766 A219767 A219768 * A219770 A219771 A219772

Keyword

nonn

Author

R. H. Hardin, Nov 27 2012

Status

approved