A224186 Number of n X 4 0..2 arrays with rows unimodal and columns nondecreasing.

46, 548, 3526, 15779, 55438, 163746, 424326, 992607, 2138488, 4305730, 8191976, 14853709, 25840868, 43366252, 70515252, 111501861, 171977322, 259398184, 383460946, 556610879, 794633026, 1117333790, 1549321930, 2120898195

Offset

1,1

Comments

Column 4 of A224190.

Links

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

Formula

Empirical: a(n) = (41/4032)*n^8 + (55/336)*n^7 + (179/160)*n^6 + (169/40)*n^5 + (615/64)*n^4 + (215/16)*n^3 + (56759/5040)*n^2 + (2173/420)*n + 1.

Conjectures from Colin Barker, Aug 29 2018: (Start)

G.f.: x*(46 + 134*x + 250*x^2 - 91*x^3 + 127*x^4 - 84*x^5 + 36*x^6 - 9*x^7 + x^8) / (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>9.

(End)

Example

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

Crossrefs

Cf. A224190.

Sequence in context: A156892 A224258 A223914 * A027940 A098227 A077732

Adjacent sequences: A224183 A224184 A224185 * A224187 A224188 A224189

Keyword

nonn

Author

R. H. Hardin, Apr 01 2013

Status

approved