A219287 Number of n X 4 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..1 n X 4 array.

4, 9, 42, 149, 423, 1092, 2623, 5937, 12729, 26009, 50896, 95774, 173920, 305737, 521743, 866485, 1403565, 2221983, 3444020, 5234902, 7814504, 11471371, 16579351, 23617153, 33191161, 46061853, 63174192, 85692374, 115039336, 152941445

Offset

1,1

Comments

Column 4 of A219291.

Links

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

Formula

Empirical: a(n) = (1/2240)*n^8 - (1/90)*n^7 + (17/96)*n^6 - (373/360)*n^5 - (4459/960)*n^4 + (49529/360)*n^3 - (348947/336)*n^2 + (55477/15)*n - 5259 for n>6.

Conjectures from Colin Barker, Jul 25 2018: (Start)

G.f.: x*(4 - 27*x + 105*x^2 - 241*x^3 + 342*x^4 - 249*x^5 + x^6 + 204*x^7 - 240*x^8 + 223*x^9 - 206*x^10 + 161*x^11 - 76*x^12 + 22*x^13 - 5*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..1..1....0..0..0..0....0..0..0..1....0..0..0..0....0..0..0..0
..0..0..0..1....0..0..0..0....0..0..0..0....0..0..0..1....0..0..0..0
..1..0..0..0....1..1..1..1....1..0..0..1....0..0..0..0....0..0..0..1

Crossrefs

Cf. A219291.

Sequence in context: A149168 A149169 A138544 * A359922 A093149 A048054

Adjacent sequences: A219284 A219285 A219286 * A219288 A219289 A219290

Keyword

nonn

Author

R. H. Hardin, Nov 17 2012

Status

approved