|
|
A220035
|
|
Number of 5 X n arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 5 X n array.
|
|
1
|
|
|
6, 10, 21, 55, 111, 192, 302, 442, 618, 838, 1111, 1447, 1857, 2353, 2948, 3656, 4492, 5472, 6613, 7933, 9451, 11187, 13162, 15398, 17918, 20746, 23907, 27427, 31333, 35653, 40416, 45652, 51392, 57668, 64513, 71961, 80047, 88807, 98278, 108498
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = (1/24)*n^4 - (1/12)*n^3 + (95/24)*n^2 + (289/12)*n - 132 for n>6.
G.f.: x*(6 - 20*x + 31*x^2 - 10*x^3 - 24*x^4 + 21*x^5 - 3*x^6 - 4*x^7 + 8*x^8 - 3*x^9 - x^10) / (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>11.
(End)
|
|
EXAMPLE
|
Some solutions for n=3:
..1..0..0....0..0..0....1..0..0....1..0..0....0..0..0....0..0..0....0..0..0
..1..1..1....1..0..0....1..0..0....1..0..0....1..0..0....1..1..0....0..0..0
..1..1..1....1..1..1....1..0..0....1..0..0....1..0..0....1..1..1....1..0..0
..1..1..1....1..1..1....1..1..1....1..0..0....1..0..0....1..1..1....1..0..0
..1..1..1....1..1..1....1..1..1....1..0..0....1..1..1....1..1..1....1..0..0
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|