A223914 Number of n X 4 0..2 arrays with rows and antidiagonals unimodal and columns nondecreasing.

46, 548, 3311, 14123, 48182, 139925, 359344, 837243, 1802306, 3633256, 6929795, 12606425, 22013660, 37091549, 60560840, 96157525, 148916916, 225513812, 334665727, 487606559, 698638490, 985770317, 1371450824, 1883406215

Offset

1,1

Comments

Column 4 of A223918.

Links

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

Formula

Empirical: a(n) = (41/4032)*n^8 + (41/336)*n^7 + (1277/1440)*n^6 + (953/240)*n^5 + (5363/576)*n^4 + (35/2)*n^3 + (28211/1680)*n^2 - (223/140)*n - 7 for n>1.

Conjectures from Colin Barker, Aug 24 2018: (Start)

G.f.: x*(46 + 134*x + 35*x^2 + 188*x^3 + 35*x^4 - 157*x^5 + 241*x^6 - 153*x^7 + 47*x^8 - 6*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..1..0..0....0..0..1..2....1..1..0..0....0..0..0..2....0..1..2..1
..1..2..2..0....0..1..1..2....1..1..2..0....0..0..2..2....0..1..2..1
..2..2..2..1....1..1..1..2....1..2..2..0....0..2..2..2....0..1..2..1

Crossrefs

Cf. A223918.

Sequence in context: A232071 A156892 A224258 * A224186 A027940 A098227

Adjacent sequences: A223911 A223912 A223913 * A223915 A223916 A223917

Keyword

nonn

Author

R. H. Hardin, Mar 29 2013

Status

approved