A223837 Number of n X 7 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

29, 239, 926, 2578, 6159, 13582, 28369, 56607, 108282, 199047, 352486, 602938, 998945, 1607388, 2518375, 3850945, 5759652, 8442093, 12147444, 17186068, 23940259, 32876186, 44557101, 59657875, 78980926, 103473603, 134247090

Offset

1,1

Comments

Column 7 of A223838.

Links

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

Formula

Empirical: a(n) = (4/315)*n^7 - (1/45)*n^6 + (28/45)*n^5 + (113/72)*n^4 + (2137/180)*n^3 + (14023/360)*n^2 + (13159/140)*n - 339 for n>4.

Conjectures from Colin Barker, Aug 23 2018: (Start)

G.f.: x*(29 + 7*x - 174*x^2 + 238*x^3 + 109*x^4 - 256*x^5 + 45*x^6 + 111*x^7 - 27*x^8 - 26*x^9 + 6*x^10 + 2*x^11) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>12.

(End)

Example

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

Crossrefs

Cf. A223838.

Sequence in context: A027112 A142095 A140845 * A126426 A126425 A224145

Adjacent sequences: A223834 A223835 A223836 * A223838 A223839 A223840

Keyword

nonn

Author

R. H. Hardin, Mar 27 2013

Status

approved