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A250521 Number of (n+1)X(2+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. 1

%I #7 Nov 14 2018 14:05:31

%S 222,1180,5029,18859,65310,214812,682921,2122743,6501118,19720580,

%T 59462069,178644459,535616774,1604254580,4803055177,14379531399,

%U 43056528118,128955131820,386326404261,1157662173067,3469836562702

%N Number of (n+1)X(2+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.

%H R. H. Hardin, <a href="/A250521/b250521.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 14*a(n-1) - 85*a(n-2) + 294*a(n-3) - 639*a(n-4) + 906*a(n-5) - 839*a(n-6) + 490*a(n-7) - 164*a(n-8) + 24*a(n-9).

%F Empirical g.f.: x*(222 - 1928*x + 7379*x^2 - 16515*x^3 + 23687*x^4 - 22151*x^5 + 13066*x^6 - 4404*x^7 + 648*x^8) / ((1 - x)^5*(1 - 2*x)^3*(1 - 3*x)). - _Colin Barker_, Nov 14 2018

%e Some solutions for n=5:

%e ..2..2..0....2..2..1....1..1..0....2..0..0....2..1..1....2..1..0....2..0..0

%e ..1..2..0....1..1..0....2..2..2....2..0..0....1..0..0....2..2..1....2..1..1

%e ..1..2..0....2..2..1....1..1..1....2..0..1....2..1..1....1..1..0....1..0..0

%e ..1..2..0....0..0..1....1..1..1....2..1..2....2..1..1....0..1..0....0..0..0

%e ..1..2..0....1..1..2....0..0..0....1..0..2....1..0..0....0..1..0....0..0..0

%e ..0..1..2....0..0..1....1..1..1....0..0..2....1..0..2....0..1..2....1..2..2

%Y Column 2 of A250527.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 24 2014

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Last modified July 23 10:53 EDT 2024. Contains 374549 sequences. (Running on oeis4.)