A250750 Number of (n+1) X (3+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.
129, 423, 1353, 4239, 13089, 40023, 121593, 367839, 1109649, 3341223, 10048233, 30193839, 90679809, 272236023, 817101273, 2452090239, 7357843569, 22076676423, 66236320713, 198721545039, 596189800929, 1788619734423, 5365959866553
Offset: 1
Keywords
Examples
Some solutions for n=4: ..1..1..1..1....0..0..0..0....0..0..0..0....2..2..2..2....1..1..1..1 ..2..2..2..2....1..1..1..2....1..1..1..1....1..1..1..1....0..0..0..0 ..1..1..1..1....0..1..1..2....2..2..2..2....1..1..1..2....2..2..2..2 ..1..1..1..1....0..1..1..2....2..2..2..2....0..0..0..1....1..1..1..1 ..0..1..2..2....0..1..1..2....0..1..2..2....0..0..0..1....1..1..1..2
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Column 3 of A250755.
Formula
Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3); a(n) = (114*3^n -48*2^n + 12)/2.
Empirical g.f.: 3*x*(43 - 117*x + 78*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - Colin Barker, Nov 17 2018