A225977 Number of n X 3 binary arrays whose sum with another n X 3 binary array containing no more than two 1s has rows and columns in lexicographically nondecreasing order.

8, 48, 252, 1178, 4722, 16361, 49811, 135672, 336189, 768900, 1642668, 3310404, 6343682, 11635425, 20537903, 35044430, 58024377, 93522432, 147134436, 226473606, 341742522, 506427905, 738136947, 1059595772, 1499832509

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..101

Formula

Empirical: a(n) = (1/4320)*n^9 + (23/6720)*n^8 + (5/336)*n^7 - (1/288)*n^6 + (659/1440)*n^5 + (443/2880)*n^4 + (80/27)*n^3 - (6203/1008)*n^2 + (2459/140)*n - 6 for n>1.

Conjectures from Colin Barker, Sep 05 2018: (Start)

G.f.: x*(8 - 32*x + 132*x^2 - 142*x^3 + 202*x^4 - 25*x^5 - 165*x^6 + 163*x^7 - 72*x^8 + 16*x^9 - x^10) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>11.

(End)

Example

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

Crossrefs

Column 3 of A225982.

Sequence in context: A069021 A079763 A079785 * A305782 A292536 A242668

Adjacent sequences: A225974 A225975 A225976 * A225978 A225979 A225980

Keyword

nonn

Author

R. H. Hardin, May 22 2013

Status

approved