A223773 Number of n X 4 0..1 arrays with rows and columns unimodal and antidiagonals nondecreasing.

11, 56, 180, 461, 1040, 2164, 4246, 7950, 14308, 24877, 41945, 68796, 110045, 172055, 263449, 395731, 584031, 847990, 1212802, 1710431, 2381022, 3274526, 4452560, 5990524, 7979998, 10531443, 13777231, 17875030, 23011571, 29406825, 37318619

Offset

1,1

Comments

Column 4 of A223777.

Links

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

Formula

Empirical: a(n) = (1/40320)*n^8 + (1/3360)*n^7 + (19/2880)*n^6 + (7/120)*n^5 + (2447/5760)*n^4 + (259/160)*n^3 + (126691/10080)*n^2 - (12329/840)*n + 13 for n>1.

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

G.f.: x*(11 - 43*x + 72*x^2 - 67*x^3 + 53*x^4 - 50*x^5 + 34*x^6 - 6*x^7 - 5*x^8 + 2*x^9) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>10.

(End)

Example

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

Crossrefs

Cf. A223777.

Sequence in context: A265151 A275643 A341405 * A224154 A079547 A034264

Adjacent sequences: A223770 A223771 A223772 * A223774 A223775 A223776

Keyword

nonn

Author

R. H. Hardin, Mar 27 2013

Status

approved