A201373 Number of n X 6 0..1 arrays with rows and columns lexicographically nondecreasing read forwards, and nonincreasing read backwards.

2, 7, 32, 157, 786, 3739, 15574, 55410, 170616, 465037, 1145954, 2597729, 5492076, 10947133, 20749996, 37660122, 65814022, 111254955, 182614908, 291980013, 455974718, 697104503, 1045401722, 1540424266, 2233662188, 3191413217

Offset

1,1

Comments

Column 6 of A201375.

Links

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

Formula

Empirical: a(n) = (1/453600)*n^10 + (1/2160)*n^9 + (227/60480)*n^8 - (73/1260)*n^7 + (1319/10800)*n^6 + (757/720)*n^5 - (881131/181440)*n^4 + (2207/540)*n^3 + (396407/25200)*n^2 - (6737/210)*n + 18.

Conjectures from Colin Barker, May 22 2018: (Start)

G.f.: x*(2 - 15*x + 65*x^2 - 140*x^3 + 324*x^4 - 166*x^5 + 20*x^6 - 349*x^7 + 391*x^8 - 142*x^9 + 18*x^10) / (1 - x)^11.

a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.

(End)

Example

Some solutions for n=5:
..0..0..0..1..1..1....0..0..0..1..1..1....0..0..0..0..1..1....0..0..1..1..1..1
..1..1..1..0..1..1....1..1..1..0..1..1....0..1..1..1..0..1....0..0..1..1..1..1
..1..1..1..1..0..1....1..1..1..1..0..1....1..0..0..1..0..1....0..1..0..1..1..1
..1..1..1..1..1..0....1..1..1..1..0..1....1..0..0..1..1..0....1..0..0..1..1..1
..1..1..1..1..1..0....1..1..1..1..1..0....1..1..1..0..0..0....1..1..1..0..0..0

Crossrefs

Cf. A201375.

Sequence in context: A334855 A334854 A047850 * A168494 A181376 A183951

Adjacent sequences: A201370 A201371 A201372 * A201374 A201375 A201376

Keyword

nonn

Author

R. H. Hardin, Nov 30 2011

Status

approved