A224136 Number of 5 X n 0..1 arrays with rows nondecreasing and antidiagonals unimodal.

32, 243, 748, 1635, 3149, 5648, 9577, 15505, 24141, 36350, 53169, 75823, 105741, 144572, 194201, 256765, 334669, 430602, 547553, 688827, 858061, 1059240, 1296713, 1575209, 1899853, 2276182, 2710161, 3208199, 3777165, 4424404, 5157753, 5985557

Offset

1,1

Comments

Row 5 of A224133.

Links

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

Formula

Empirical: a(n) = (2/15)*n^5 + (7/6)*n^4 + (47/6)*n^3 + (173/6)*n^2 + (1981/30)*n - 27 for n>3.

Conjectures from Colin Barker, Aug 27 2018: (Start)

G.f.: x*(32 + 51*x - 230*x^2 + 152*x^3 + 179*x^4 - 228*x^5 + 18*x^6 + 63*x^7 - 21*x^8) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>9.

(End)

Example

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

Crossrefs

Cf. A224133.

Sequence in context: A104782 A186774 A223952 * A250363 A346637 A017674

Adjacent sequences: A224133 A224134 A224135 * A224137 A224138 A224139

Keyword

nonn

Author

R. H. Hardin, Mar 31 2013

Status

approved