A223772 Number of n X 3 0..1 arrays with rows and columns unimodal and antidiagonals nondecreasing.

7, 28, 78, 180, 371, 707, 1269, 2170, 3563, 5650, 8692, 13020, 19047, 27281, 38339, 52962, 72031, 96584, 127834, 167188, 216267, 276927, 351281, 441722, 550947, 681982, 838208, 1023388, 1241695, 1497741, 1796607, 2143874, 2545655, 3008628

Offset

1,1

Comments

Column 3 of A223777.

Links

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

Formula

Empirical: a(n) = (1/720)*n^6 + (1/80)*n^5 + (29/144)*n^4 + (25/48)*n^3 + (1727/360)*n^2 - (8/15)*n + 2.

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

G.f.: x*(7 - 21*x + 29*x^2 - 23*x^3 + 14*x^4 - 7*x^5 + 2*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..1....1..0..0....1..1..1....1..0..0....1..0..0....0..0..0....0..1..0
..1..1..0....1..0..0....1..1..1....1..0..0....1..0..0....0..1..0....1..1..0
..1..0..0....0..0..0....1..1..1....1..1..0....1..1..1....1..1..1....1..0..0

Crossrefs

Cf. A223777.

Sequence in context: A341986 A341067 A061968 * A024012 A352900 A163705

Adjacent sequences: A223769 A223770 A223771 * A223773 A223774 A223775

Keyword

nonn

Author

R. H. Hardin, Mar 27 2013

Status

approved