A224144 Number of n X 6 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

22, 148, 554, 1573, 3827, 8375, 16885, 31841, 56783, 96579, 157729, 248701, 380299, 566063, 822701, 1170553, 1634087, 2242427, 3029913, 4036693, 5309347, 6901543, 8874725, 11298833, 14253055, 17826611, 22119569, 27243693, 33323323, 40496287

Offset

1,1

Comments

Column 6 of A224146.

Links

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

Formula

Empirical: a(n) = (2/45)*n^6 + (4/15)*n^5 + (16/9)*n^4 + 6*n^3 + (683/45)*n^2 + (341/15)*n - 55 for n>3.

Conjectures from Colin Barker, Aug 28 2018: (Start)

G.f.: x*(22 - 6*x - 20*x^2 + 33*x^3 + 40*x^4 - 53*x^5 + 8*x^6 + 11*x^7 - 2*x^8 - x^9) / (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>10.

(End)

Example

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

Crossrefs

Cf. A224146.

Sequence in context: A262139 A159505 A223836 * A225008 A240384 A245380

Adjacent sequences: A224141 A224142 A224143 * A224145 A224146 A224147

Keyword

nonn

Author

R. H. Hardin, Mar 31 2013

Status

approved