A253455 Number of (n+1) X (7+1) 0..2 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally and vertically.

48293, 74324, 89556, 114717, 170184, 285681, 526430, 1036512, 2142374, 4611192, 10320110, 24051792, 58456694, 148091112, 389833790, 1060740672, 2964819014, 8459769432, 24510051470, 71791759152, 211898605334, 628742590152

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..147

Formula

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

Empirical: a(n) = 529*3^(n-3) + 6631*2^(n-1) + 59197 for n>6.

Empirical g.f.: x*(48293 - 215434*x + 174835*x^2 + 105187*x^3 + 21054*x^4 - 10872*x^5 - 3934*x^6 - 681*x^7 - 54*x^8) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - Colin Barker, Dec 13 2018

Example

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

Crossrefs

Column 7 of A253456.

Sequence in context: A227701 A253494 A253501 * A233890 A031867 A151839

Adjacent sequences: A253452 A253453 A253454 * A253456 A253457 A253458

Keyword

nonn

Author

R. H. Hardin, Jan 01 2015

Status

approved