A223756 Number of n X 2 0..3 arrays with rows, antidiagonals and columns unimodal.

16, 256, 2500, 16900, 87616, 372100, 1352569, 4338889, 12559936, 33362176, 82373776, 190992400, 419266576, 877225924, 1759047481, 3396208729, 6338070544, 11471266816, 20192978404, 34657779556, 58123423744, 95427859396

Offset

1,1

Comments

Column 2 of A223762.

Links

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

Formula

Empirical: a(n) = (1/518400)*n^12 + (1/17280)*n^11 + (91/103680)*n^10 + (71/8640)*n^9 + (9101/172800)*n^8 + (457/1920)*n^7 + (81397/103680)*n^6 + (497/270)*n^5 + (203687/64800)*n^4 + (1933/540)*n^3 + (2533/720)*n^2 + (11/6)*n + 1.

a(n) = A223659(n)^2. - Mark van Hoeij, May 14 2013

Conjectures from Colin Barker, Feb 19 2018: (Start)

G.f.: x*(16 + 48*x + 420*x^2 - 208*x^3 + 1140*x^4 - 1260*x^5 + 1401*x^6 - 1044*x^7 + 597*x^8 - 244*x^9 + 69*x^10 - 12*x^11 + x^12) / (1 - x)^13.

a(n) = 13*a(n-1) - 78*a(n-2) + 286*a(n-3) - 715*a(n-4) + 1287*a(n-5) - 1716*a(n-6) + 1716*a(n-7) - 1287*a(n-8) + 715*a(n-9) - 286*a(n-10) + 78*a(n-11) - 13*a(n-12) + a(n-13) for n>13.

(End)

Example

Some solutions for n=3:
..3..2....0..0....0..0....1..2....0..3....2..1....1..3....0..0....3..1....3..1
..2..0....1..1....1..2....3..2....1..3....2..3....3..3....0..0....1..0....2..3
..2..0....3..0....1..2....0..0....2..1....1..3....3..2....0..3....1..0....0..3

Crossrefs

Sequence in context: A189191 A188876 A223634 * A188905 A189106 A189112

Adjacent sequences: A223753 A223754 A223755 * A223757 A223758 A223759

Keyword

nonn

Author

R. H. Hardin, Mar 27 2013

Status

approved