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

1,1

Comments

Column 4 of A250432

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

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

Sequence in context: A204391 A233903 A233897 * A033696 A233653 A233646

Adjacent sequences: A250425 A250426 A250427 * A250429 A250430 A250431

Keyword

nonn

Author

R. H. Hardin, Nov 22 2014

Status

approved