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

1,1

Comments

Column 3 of A250432

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

Example

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

Crossrefs

Sequence in context: A237405 A250443 A017162 * A236828 A236821 A237511

Adjacent sequences: A250424 A250425 A250426 * A250428 A250429 A250430

Keyword

nonn

Author

R. H. Hardin, Nov 22 2014

Status

approved