|
|
A223640
|
|
Number of n X 4 0..1 arrays with rows, columns, diagonals and antidiagonals unimodal.
|
|
1
|
|
|
11, 121, 726, 2962, 9808, 28450, 74599, 179991, 404599, 855417, 1714062, 3275798, 6002946, 10596004, 18086161, 29953249, 48273537, 75902131, 116695104, 175776840, 259858436, 377613366, 540116971, 761356699, 1058820379, 1454170173
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = (1/112)*n^8 - (19/210)*n^7 + (107/90)*n^6 - (197/40)*n^5 + (2219/144)*n^4 + (5093/120)*n^3 - (868411/2520)*n^2 + (417721/420)*n - 1091 for n>4.
G.f.: x*(11 + 22*x + 33*x^2 - 140*x^3 + 508*x^4 - 314*x^5 - 17*x^6 + 432*x^7 - 233*x^8 + 28*x^9 + 56*x^10 - 28*x^11 + 2*x^12) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>13.
(End)
|
|
EXAMPLE
|
Some solutions for n=4:
..0..1..0..0....1..1..0..0....1..0..0..0....0..1..1..1....0..0..1..1
..0..1..1..1....1..1..1..0....0..1..0..0....0..0..1..1....0..1..1..1
..0..1..1..0....0..1..1..1....0..0..0..0....0..0..0..0....0..0..0..0
..0..0..1..0....0..0..0..1....0..0..1..0....0..0..0..0....0..0..0..0
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|