A253500 Number of (6+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.

19701, 22236, 29370, 40117, 63550, 113573, 220988, 457436, 995132, 2264924, 5387708, 13382876, 34622012, 92846684, 256535228, 725629916, 2088972092, 6091114844, 17921775548, 53062222556, 157780493372, 470529165404

Offset

1,1

Links

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

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) + 2682*2^(n-1) + 16940 for n>6.

Empirical g.f.: x*(19701 - 95970*x + 112665*x^2 - 9713*x^3 + 12502*x^4 - 2660*x^5 - 2102*x^6 - 489*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..2..2....0..0..0..1..0....0..1..0..0..0....1..1..2..1..2
..2..2..2..2..2....1..1..1..2..1....0..1..0..0..0....1..0..1..0..1
..0..0..0..0..0....0..0..0..1..0....1..2..1..1..1....1..0..1..0..1
..2..2..2..2..2....0..0..0..1..0....0..1..0..0..0....1..0..1..0..1
..2..2..2..2..2....0..0..0..1..0....1..2..1..1..1....1..0..1..0..1
..1..1..1..1..1....0..0..0..1..0....0..1..0..0..0....1..0..1..0..1
..1..1..1..1..1....0..0..0..2..2....0..1..0..0..2....1..0..1..0..2

Crossrefs

Row 6 of A253495.

Sequence in context: A081866 A288885 A253493 * A253454 A237096 A252206

Adjacent sequences: A253497 A253498 A253499 * A253501 A253502 A253503

Keyword

nonn

Author

R. H. Hardin, Jan 02 2015

Status

approved