A201371 - OEIS

A201371

Number of n X 4 0..1 arrays with rows and columns lexicographically nondecreasing read forwards, and nonincreasing read backwards.

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

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OFFSET

1,1

COMMENTS

Column 4 of A201375.

LINKS

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

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

Adjacent sequences: A201368 A201369 A201370 * A201372 A201373 A201374

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 30 2011

STATUS

approved