A223951 Number of 4 X n 0..1 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

16, 81, 177, 321, 558, 928, 1479, 2267, 3356, 4818, 6733, 9189, 12282, 16116, 20803, 26463, 33224, 41222, 50601, 61513, 74118, 88584, 105087, 123811, 144948, 168698, 195269, 224877, 257746, 294108, 334203, 378279, 426592, 479406, 536993, 599633

Offset

1,1

Comments

Row 4 of A223949.

Links

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

Formula

Empirical: a(n) = (1/3)*n^4 + (2/3)*n^3 + (37/6)*n^2 + (107/6)*n + 23 for n>2.

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

G.f.: x*(16 + x - 68*x^2 + 86*x^3 - 7*x^4 - 33*x^5 + 13*x^6) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>7.

(End)

Example

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

Crossrefs

Cf. A223949.

Sequence in context: A065771 A320965 A295071 * A041490 A096020 A016898

Adjacent sequences: A223948 A223949 A223950 * A223952 A223953 A223954

Keyword

nonn

Author

R. H. Hardin, Mar 29 2013

Status

approved