login
A201371
Number of n X 4 0..1 arrays with rows and columns lexicographically nondecreasing read forwards, and nonincreasing read backwards.
1
2, 5, 14, 36, 80, 157, 280, 464, 726, 1085, 1562, 2180, 2964, 3941, 5140, 6592, 8330, 10389, 12806, 15620, 18872, 22605, 26864, 31696, 37150, 43277, 50130, 57764, 66236, 75605, 85932, 97280, 109714, 123301, 138110, 154212, 171680, 190589, 211016
OFFSET
1,1
COMMENTS
Column 4 of A201375.
LINKS
FORMULA
Empirical: a(n) = (1/12)*n^4 + (1/3)*n^3 - (13/12)*n^2 + (8/3)*n.
Conjectures from Colin Barker, May 22 2018: (Start)
G.f.: x*(2 - 5*x + 9*x^2 - 4*x^3) / (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>5.
(End)
EXAMPLE
Some solutions for n=5:
..0..0..1..1....0..0..1..1....0..1..1..1....0..1..1..1....0..0..0..1
..0..0..1..1....0..0..1..1....1..0..1..1....0..1..1..1....0..0..0..1
..1..1..0..1....0..1..0..1....1..1..0..0....1..0..0..1....0..0..0..1
..1..1..1..0....0..1..1..0....1..1..0..0....1..1..1..0....0..0..1..0
..1..1..1..0....1..0..0..0....1..1..0..0....1..1..1..0....1..1..0..0
CROSSREFS
Cf. A201375.
Sequence in context: A137917 A360031 A244099 * A244061 A297120 A299167
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 30 2011
STATUS
approved