login
A225009
Number of n X 7 0..1 arrays with rows unimodal and columns nondecreasing.
1
29, 239, 1163, 4166, 12174, 30738, 69498, 144111, 278707, 508937, 885677, 1479452, 2385644, 3730548, 5678340, 8439021, 12277401, 17523187, 24582239, 33949058, 46220570, 62111270, 82469790, 108296955, 140765391, 181240749, 231304609
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = (4/315)*n^7 + (1/5)*n^6 + (58/45)*n^5 + (35/8)*n^4 + (1507/180)*n^3 + (357/40)*n^2 + (2027/420)*n + 1.
Conjectures from Colin Barker, Sep 05 2018: (Start)
G.f.: x*(29 + 7*x + 63*x^2 - 70*x^3 + 56*x^4 - 28*x^5 + 8*x^6 - x^7) / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
(End)
EXAMPLE
Some solutions for n=3:
..0..1..1..0..0..0..0....1..1..1..1..0..0..0....0..0..0..0..0..0..0
..0..1..1..1..1..0..0....1..1..1..1..1..0..0....1..1..0..0..0..0..0
..1..1..1..1..1..1..1....1..1..1..1..1..1..1....1..1..0..0..0..0..0
CROSSREFS
Column 7 of A225010.
Sequence in context: A126426 A126425 A224145 * A177419 A142559 A125366
KEYWORD
nonn
AUTHOR
R. H. Hardin, Apr 23 2013
STATUS
approved