A250427 Number of (n+1)X(3+1) 0..1 arrays with nondecreasing sum of every two consecutive values in every row and column.

81, 324, 1296, 3600, 10000, 22500, 50625, 99225, 194481, 345744, 614656, 1016064, 1679616, 2624400, 4100625, 6125625, 9150625, 13176900, 18974736, 26501904, 37015056, 50381604, 68574961, 91298025, 121550625, 158760000, 207360000

Offset: 1

Author

R. H. Hardin, Nov 22 2014

Keywords

• nonn

Comments

Column 3 of A250432

Examples

			Some solutions for n=6
..0..0..0..0....0..0..0..1....0..0..1..1....0..0..0..0....0..0..1..0
..0..0..1..1....0..0..0..0....0..0..1..0....0..0..0..1....0..0..1..0
..0..0..1..0....0..0..0..1....0..0..1..1....0..0..1..1....0..0..1..1
..0..0..1..1....0..0..0..1....0..0..1..0....0..0..0..1....1..0..1..0
..0..0..1..1....0..0..1..1....0..1..1..1....0..0..1..1....0..0..1..1
..1..0..1..1....0..0..1..1....1..0..1..0....0..0..0..1....1..0..1..0
..1..0..1..1....1..1..1..1....0..1..1..1....0..1..1..1....1..1..1..1
		

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +6*a(n-2) -14*a(n-3) -14*a(n-4) +42*a(n-5) +14*a(n-6) -70*a(n-7) +70*a(n-9) -14*a(n-10) -42*a(n-11) +14*a(n-12) +14*a(n-13) -6*a(n-14) -2*a(n-15) +a(n-16)

Empirical for n mod 2 = 0: a(n) = (1/4096)*n^8 + (1/128)*n^7 + (55/512)*n^6 + (53/64)*n^5 + (1001/256)*n^4 + (185/16)*n^3 + (167/8)*n^2 + 21*n + 9

Empirical for n mod 2 = 1: a(n) = (1/4096)*n^8 + (1/128)*n^7 + (111/1024)*n^6 + (109/128)*n^5 + (8483/2048)*n^4 + (1635/128)*n^3 + (24975/1024)*n^2 + (3375/128)*n + (50625/4096).

a(n+1) = A202094(n). - R. J. Mathar, Dec 04 2014