

A223833


Number of n X 3 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.


1



7, 22, 48, 89, 149, 232, 342, 483, 659, 874, 1132, 1437, 1793, 2204, 2674, 3207, 3807, 4478, 5224, 6049, 6957, 7952, 9038, 10219, 11499, 12882, 14372, 15973, 17689, 19524, 21482, 23567, 25783, 28134, 30624, 33257, 36037, 38968, 42054, 45299, 48707, 52282
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OFFSET

1,1


COMMENTS

Column 3 of A223838.


LINKS

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


FORMULA

Empirical: a(n) = (2/3)*n^3 + (3/2)*n^2 + (35/6)*n  1.
Conjectures from Colin Barker, Aug 23 2018: (Start)
G.f.: x*(7  6*x + 2*x^2 + x^3) / (1  x)^4.
a(n) = 4*a(n1)  6*a(n2) + 4*a(n3)  a(n4) for n>4.
(End)


EXAMPLE

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


CROSSREFS

Cf. A223838.
Sequence in context: A331229 A299283 A244243 * A014073 A288114 A129109
Adjacent sequences: A223830 A223831 A223832 * A223834 A223835 A223836


KEYWORD

nonn


AUTHOR

R. H. Hardin, Mar 27 2013


STATUS

approved



