A224040 Number of 4 X n 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

16, 55, 105, 168, 252, 363, 508, 695, 933, 1232, 1603, 2058, 2610, 3273, 4062, 4993, 6083, 7350, 8813, 10492, 12408, 14583, 17040, 19803, 22897, 26348, 30183, 34430, 39118, 44277, 49938, 56133, 62895, 70258, 78257, 86928, 96308, 106435, 117348

Offset

1,1

Comments

Row 4 of A224038.

Links

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

Formula

Empirical: a(n) = (1/24)*n^4 + (1/4)*n^3 + (83/24)*n^2 + (89/4)*n - 3 for n>2.

Conjectures from Colin Barker, Aug 26 2018: (Start)

G.f.: x*(16 - 25*x - 10*x^2 + 33*x^3 - 8*x^4 - 8*x^5 + 3*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:
..1..1..1....1..1..1....0..0..1....0..1..1....0..0..1....0..0..0....1..1..1
..1..1..1....0..1..1....1..1..1....0..1..1....1..1..1....0..0..1....0..1..1
..1..1..1....0..1..1....0..1..1....0..1..1....1..1..1....1..1..1....0..0..1
..0..1..1....0..1..1....0..0..1....0..0..1....1..1..1....0..1..1....0..0..1

Crossrefs

Cf. A224038.

Sequence in context: A297842 A172190 A122658 * A244805 A362039 A188838

Adjacent sequences: A224037 A224038 A224039 * A224041 A224042 A224043

Keyword

nonn

Author

R. H. Hardin, Mar 30 2013

Status

approved