|
|
A250428
|
|
Number of (n+1)X(4+1) 0..1 arrays with nondecreasing sum of every two consecutive values in every row and column
|
|
1
|
|
|
144, 720, 3600, 12000, 40000, 105000, 275625, 617400, 1382976, 2765952, 5531904, 10160640, 18662400, 32076000, 55130625, 89842500, 146410000, 228399600, 356303376, 535927392, 806105664, 1175570760, 1714374025, 2434614000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = 2*a(n-1) +8*a(n-2) -18*a(n-3) -27*a(n-4) +72*a(n-5) +48*a(n-6) -168*a(n-7) -42*a(n-8) +252*a(n-9) -252*a(n-11) +42*a(n-12) +168*a(n-13) -48*a(n-14) -72*a(n-15) +27*a(n-16) +18*a(n-17) -8*a(n-18) -2*a(n-19) +a(n-20)
Empirical for n mod 2 = 0: a(n) = (1/147456)*n^10 + (23/73728)*n^9 + (13/2048)*n^8 + (77/1024)*n^7 + (1763/3072)*n^6 + (4525/1536)*n^5 + (5927/576)*n^4 + (3473/144)*n^3 + (145/4)*n^2 + (63/2)*n + 12
Empirical for n mod 2 = 1: a(n) = (1/147456)*n^10 + (23/73728)*n^9 + (941/147456)*n^8 + (1409/18432)*n^7 + (43777/73728)*n^6 + (115189/36864)*n^5 + (831857/73728)*n^4 + (169595/6144)*n^3 + (717525/16384)*n^2 + (333375/8192)*n + (275625/16384).
|
|
EXAMPLE
|
Some solutions for n=6
..0..0..0..1..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
..0..0..0..0..1....0..0..0..1..0....0..1..0..1..1....0..0..0..1..1
..0..0..1..1..1....0..0..0..1..0....0..0..0..0..0....0..0..1..0..1
..0..1..0..1..1....0..0..0..1..1....1..1..1..1..1....0..1..0..1..1
..1..0..1..1..1....0..1..0..1..1....0..0..1..0..1....1..0..1..0..1
..1..1..1..1..1....0..0..0..1..1....1..1..1..1..1....0..1..1..1..1
..1..1..1..1..1....0..1..0..1..1....0..0..1..1..1....1..0..1..1..1
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|