|
|
A224041
|
|
Number of 5 X n 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.
|
|
1
|
|
|
32, 144, 298, 488, 734, 1064, 1505, 2091, 2864, 3875, 5185, 6866, 9002, 11690, 15041, 19181, 24252, 30413, 37841, 46732, 57302, 69788, 84449, 101567, 121448, 144423, 170849, 201110, 235618, 274814, 319169, 369185, 425396, 488369, 558705, 637040
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = (1/120)*n^5 + (1/24)*n^4 + (25/24)*n^3 + (227/24)*n^2 + (1289/20)*n - 7 for n>3.
G.f.: x*(32 - 48*x - 86*x^2 + 220*x^3 - 124*x^4 - 12*x^5 + 9*x^6 + 17*x^7 - 7*x^8) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>9.
(End)
|
|
EXAMPLE
|
Some solutions for n=3:
..0..0..1....0..0..0....1..1..1....0..0..1....1..1..1....0..0..0....0..1..1
..0..0..0....0..0..0....0..1..1....0..0..0....1..1..1....0..0..1....0..1..1
..0..0..1....0..1..1....0..1..1....0..0..0....0..1..1....0..0..1....0..1..1
..0..1..1....1..1..1....0..1..1....0..0..0....1..1..1....0..0..0....0..1..1
..0..0..1....1..1..1....0..1..1....0..1..1....0..1..1....0..1..1....1..1..1
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|