A219572 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..3 n X 2 array.

4, 13, 59, 181, 469, 1107, 2447, 5120, 10197, 19415, 35485, 62501, 106471, 175993, 283101, 444308, 681875, 1025337, 1513319, 2195677, 3136001, 4414519, 6131443, 8410800, 11404793, 15298739, 20316633, 26727389, 34851811, 45070349, 57831697

Offset

1,1

Comments

Column 2 of A219578.

Links

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

Formula

Empirical: a(n) = (1/20160)*n^8 + (1/2520)*n^7 + (1/480)*n^6 + (43/360)*n^5 - (297/320)*n^4 + (1271/180)*n^3 - (75973/5040)*n^2 + (2081/105)*n - 12 for n>1.

Conjectures from Colin Barker, Mar 11 2018: (Start)

G.f.: x*(4 - 23*x + 86*x^2 - 218*x^3 + 376*x^4 - 420*x^5 + 296*x^6 - 127*x^7 + 33*x^8 - 5*x^9) / (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>10.

(End)

Example

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

Crossrefs

Cf. A219578.

Sequence in context: A149485 A006798 A158267 * A026663 A149486 A317891

Adjacent sequences: A219569 A219570 A219571 * A219573 A219574 A219575

Keyword

nonn

Author

R. H. Hardin, Nov 23 2012

Status

approved