A253501 Number of (7+1) X (n+1) 0..2 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally.

48293, 55362, 68992, 89339, 133284, 224747, 415106, 817442, 1686914, 3620258, 8070146, 18719522, 45267074, 114108578, 299030786, 810592802, 2258869634, 6430881698, 18601281026, 54421205282, 160498430594, 475965011618

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..201

Formula

Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n>9.

Empirical: a(n) = 400*3^(n-3) + 5274*2^(n-1) + 45170 for n>6.

Empirical g.f.: x*(48293 - 234396*x + 268043*x^2 - 5389*x^3 + 23990*x^4 - 6180*x^5 - 3286*x^6 - 681*x^7 - 54*x^8) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - Colin Barker, Dec 16 2018

Example

Some solutions for n=4:
..1..2..2..1..1....2..2..2..2..1....2..2..2..2..2....0..1..2..2..2
..0..1..1..0..0....2..2..2..2..1....2..2..2..2..2....2..2..2..2..2
..1..2..2..1..1....1..1..1..1..0....1..1..1..1..1....0..0..0..0..0
..0..1..1..0..0....2..2..2..2..1....2..2..2..2..2....0..0..0..0..0
..1..2..2..1..1....1..1..1..1..0....2..2..2..2..2....1..1..1..1..1
..1..2..2..1..1....2..2..2..2..1....1..1..1..1..1....2..2..2..2..2
..1..2..2..1..1....1..1..1..1..0....2..2..2..2..2....0..0..0..0..0
..0..1..1..0..1....1..1..1..1..2....0..0..0..1..2....0..0..0..0..0

Crossrefs

Row 7 of A253495.

Sequence in context: A221556 A227701 A253494 * A253455 A233890 A031867

Adjacent sequences: A253498 A253499 A253500 * A253502 A253503 A253504

Keyword

nonn

Author

R. H. Hardin, Jan 02 2015

Status

approved