A223766 Number of n X 4 0..1 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing

11, 56, 155, 361, 782, 1601, 3141, 5907, 10678, 18618, 31422, 51505, 82243, 128276, 195884, 293448, 432009, 625939, 893739, 1258980, 1751404, 2408203, 3275495, 4410017, 5881056, 7772640, 10186012, 13242411, 17086185, 21888262, 27850006

Offset

1,1

Comments

Column 4 of A223770.

Links

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

Formula

Empirical: a(n) = (1/40320)*n^8 - (1/10080)*n^7 + (3/320)*n^6 + (1/45)*n^5 + (1109/1920)*n^4 - (4837/1440)*n^3 + (422483/10080)*n^2 - (109337/840)*n + 226 for n>4.

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

G.f.: x*(11 - 43*x + 47*x^2 + 58*x^3 - 205*x^4 + 209*x^5 - 42*x^6 - 150*x^7 + 256*x^8 - 245*x^9 + 151*x^10 - 55*x^11 + 9*x^12) / (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>13.

(End)

Example

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

Crossrefs

Cf. A223770.

Sequence in context: A099532 A041226 A042503 * A265151 A275643 A341405

Adjacent sequences: A223763 A223764 A223765 * A223767 A223768 A223769

Keyword

nonn

Author

R. H. Hardin, Mar 27 2013

Status

approved