|
|
A253001
|
|
Number of n X 5 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 3 and every value within 3 of its king move distance from the upper left and every value increasing by 0 or 1 with every step right, diagonally se or down.
|
|
1
|
|
|
4, 14, 34, 69, 69, 3072, 39758, 228484, 775433, 1932763, 3965261, 7139167, 11720721, 17976163, 26171733, 36573671, 49448217, 65061611, 83680093, 105569903, 130997281, 160228467, 193529701, 231167223, 273407273, 320516091, 372759917
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = (133120/3)*n^3 - 893616*n^2 + (18332582/3)*n - 14187577 for n>8.
G.f.: x*(4 - 2*x + 2*x^2 + x^3 - 55*x^4 + 3088*x^5 + 27642*x^6 + 87677*x^7 + 87826*x^8 + 45975*x^9 + 12629*x^10 + 1453*x^11) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>12.
(End)
|
|
EXAMPLE
|
Some solutions for n=6:
..0..0..0..1..2....0..0..0..1..2....0..0..0..0..1....0..0..1..1..1
..1..1..1..1..2....0..1..1..1..2....0..0..1..1..1....0..0..1..1..1
..1..1..2..2..2....1..1..1..1..2....0..1..1..1..1....1..1..1..2..2
..1..2..2..2..2....1..1..1..1..2....1..1..1..1..2....1..1..1..2..2
..1..2..2..2..2....2..2..2..2..2....1..1..1..2..2....2..2..2..2..2
..2..2..2..2..2....2..2..2..2..2....2..2..2..2..2....2..2..2..2..2
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|