A225008 Number of n X 6 0..1 arrays with rows unimodal and columns nondecreasing.

22, 148, 610, 1897, 4900, 11088, 22716, 43065, 76714, 129844, 210574, 329329, 499240, 736576, 1061208, 1497105, 2072862, 2822260, 3784858, 5006617, 6540556, 8447440, 10796500, 13666185, 17144946, 21332052, 26338438, 32287585, 39316432

Offset

1,1

Links

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

Formula

Empirical: a(n) = (2/45)*n^6 + (8/15)*n^5 + (91/36)*n^4 + 6*n^3 + (1337/180)*n^2 + (67/15)*n + 1.

Conjectures from Colin Barker, Sep 05 2018: (Start)

G.f.: x*(22 - 6*x + 36*x^2 - 35*x^3 + 21*x^4 - 7*x^5 + x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

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

Crossrefs

Column 6 of A225010.

Sequence in context: A159505 A223836 A224144 * A240384 A245380 A271635

Adjacent sequences: A225005 A225006 A225007 * A225009 A225010 A225011

Keyword

nonn

Author

R. H. Hardin, Apr 23 2013

Status

approved