login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, May 22 2013
STATUS
approved