A266471 Number of 4 X n binary arrays with rows and columns lexicographically nondecreasing and column sums nonincreasing.

5, 12, 29, 66, 137, 261, 463, 775, 1237, 1898, 2817, 4064, 5721, 7883, 10659, 14173, 18565, 23992, 30629, 38670, 48329, 59841, 73463, 89475, 108181, 129910, 155017, 183884, 216921, 254567, 297291, 345593, 400005, 461092, 529453, 605722, 690569

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/120)*n^5 + (1/24)*n^4 + (17/24)*n^3 - (25/24)*n^2 + (257/60)*n + 1.

Conjectures from Colin Barker, Jan 10 2019: (Start)

G.f.: x*(5 - 18*x + 32*x^2 - 28*x^3 + 11*x^4 - x^5) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Example

Some solutions for n=4:
..0..0..0..0....0..0..0..0....0..1..1..1....0..0..0..0....0..0..1..1
..0..0..0..0....0..0..0..0....1..0..0..0....0..0..1..1....0..1..0..0
..1..1..1..1....0..0..0..0....1..0..1..1....1..1..0..0....1..0..0..0
..1..1..1..1....1..1..1..1....1..1..0..0....1..1..1..1....1..1..1..1

Crossrefs

Row 4 of A266470.

Sequence in context: A196410 A000465 A283506 * A069306 A277088 A009412

Adjacent sequences: A266468 A266469 A266470 * A266472 A266473 A266474

Keyword

nonn

Author

R. H. Hardin, Dec 29 2015

Status

approved