A250428 Number of (n+1)X(4+1) 0..1 arrays with nondecreasing sum of every two consecutive values in every row and column.
144, 720, 3600, 12000, 40000, 105000, 275625, 617400, 1382976, 2765952, 5531904, 10160640, 18662400, 32076000, 55130625, 89842500, 146410000, 228399600, 356303376, 535927392, 806105664, 1175570760, 1714374025, 2434614000
Offset: 1
Keywords
Examples
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
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
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).
a(n+1)=A202095(n). - R. J. Mathar, Dec 04 2014
Comments