A223836 Number of n X 6 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

22, 148, 503, 1286, 2884, 5992, 11749, 21912, 39064, 66854, 110269, 175938, 272468, 410812, 604669, 870916, 1230072, 1706794, 2330405, 3135454, 4162308, 5457776, 7075765, 9077968, 11534584, 14525070, 18138925, 22476506, 27649876, 33783684

Offset

1,1

Comments

Column 6 of A223838.

Links

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

Formula

Empirical: a(n) = (2/45)*n^6 + (55/36)*n^4 + (14/3)*n^3 + (3767/180)*n^2 + (293/6)*n - 116 for n>3.

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

G.f.: x*(22 - 6*x - 71*x^2 + 103*x^3 + 35*x^4 - 77*x^5 + 10*x^6 + 22*x^7 - 4*x^8 - 2*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..0..0..0..0..1....0..1..1..0..0..0....0..0..0..0..0..0....0..0..0..1..1..0
..0..0..1..1..1..1....1..1..1..1..0..0....0..1..0..0..0..0....0..0..0..1..1..0
..1..1..1..1..1..1....1..1..1..1..1..1....1..1..1..1..1..1....0..0..1..1..1..1

Crossrefs

Cf. A223838.

Sequence in context: A169722 A262139 A159505 * A224144 A225008 A240384

Adjacent sequences: A223833 A223834 A223835 * A223837 A223838 A223839

Keyword

nonn

Author

R. H. Hardin, Mar 27 2013

Status

approved