A223711 Number of n X 2 0..1 arrays with row sums and column sums unimodal.

4, 16, 53, 155, 418, 1066, 2611, 6205, 14408, 32852, 73825, 163951, 360574, 786574, 1704095, 3670193, 7864516, 16777432, 35651821, 75497731, 159383834, 335544626, 704643403, 1476395365, 3087008128, 6442451356, 13421773241, 27917287895

Offset

1,1

Comments

Column 2 of A223716.

Links

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

Formula

Empirical: a(n) = 7*a(n-1) - 19*a(n-2) + 25*a(n-3) - 16*a(n-4) + 4*a(n-5).

Conjectures from Colin Barker, Mar 16 2018: (Start)

G.f.: x*(2 - 3*x + 2*x^2)^2 / ((1 - x)^3*(1 - 2*x)^2).

a(n) = (-2*(2^(3+n)-9) + (5+2^(3+n))*n + n^2) / 2.

(End)

Example

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

Crossrefs

Cf. A223716.

Sequence in context: A220936 A232399 A087972 * A074409 A056589 A074407

Adjacent sequences: A223708 A223709 A223710 * A223712 A223713 A223714

Keyword

nonn

Author

R. H. Hardin, Mar 26 2013

Status

approved