A250728 Number of (n+1)X(7+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

1302, 3173, 6257, 11377, 19887, 34069, 57397, 95231, 155263, 248537, 390263, 601256, 909242, 1350837, 1973466, 2838027, 4021571, 5620807, 7755707, 10574024, 14256002, 19020095, 25128978, 32896671, 42696063, 54967661, 70228855, 89084528

Offset: 1

Author

R. H. Hardin, Nov 27 2014

Keywords

• nonn

Comments

Column 7 of A250729

Examples

			Some solutions for n=4
..0..0..0..0..0..0..0..0....0..0..0..0..0..0..0..1....0..0..0..0..0..0..0..1
..0..0..0..0..0..0..0..1....0..0..0..0..0..0..0..1....0..0..0..0..0..0..1..1
..0..0..0..0..0..1..1..1....0..0..0..0..0..0..0..1....0..0..0..0..0..1..1..1
..0..0..0..0..0..1..1..1....0..0..0..0..1..0..0..1....0..0..0..0..0..1..1..1
..0..0..0..0..1..1..1..1....1..1..0..1..0..1..0..1....1..0..1..1..0..1..1..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 8*a(n-1) -27*a(n-2) +48*a(n-3) -42*a(n-4) +42*a(n-6) -48*a(n-7) +27*a(n-8) -8*a(n-9) +a(n-10) for n>17

Empirical for n mod 2 = 0: a(n) = (1/20160)*n^8 + (1/420)*n^7 + (71/1440)*n^6 + (71/120)*n^5 + (17767/2880)*n^4 + (1159/120)*n^3 + (533033/1680)*n^2 + (86336/105)*n - 5 for n>7

Empirical for n mod 2 = 1: a(n) = (1/20160)*n^8 + (1/420)*n^7 + (71/1440)*n^6 + (71/120)*n^5 + (17767/2880)*n^4 + (1159/120)*n^3 + (533033/1680)*n^2 + (86336/105)*n - 17 for n>7