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A250875 Number of (n+1) X (6+1) 0..3 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

%S 3680,18520,88212,400496,1755220,7500960,31484612,130461616,535577460,

%T 2183825600,8860495012,35818848336,144408578900,581039033440,

%U 2334380609412,9368216508656,37564989535540,150536411220480

%N Number of (n+1) X (6+1) 0..3 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="/A250875/b250875.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4); a(n) = (6608*4^n - 6426*3^n + 1890*2^n + 106)/3.

%F Empirical g.f.: 4*x*(920 - 4570*x + 7953*x^2 - 4356*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)). - _Colin Barker_, Nov 22 2018

%e Some solutions for n=3:

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

%e ..0..0..0..0..1..1..1....3..3..3..3..3..3..3....1..2..2..3..3..3..3

%e ..0..0..0..0..1..1..1....0..0..0..0..0..1..1....1..2..2..3..3..3..3

%e ..0..1..1..1..2..2..2....0..1..1..1..1..2..3....0..1..1..2..2..3..3

%Y Column 6 of A250877.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 28 2014

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Last modified October 1 13:48 EDT 2022. Contains 357149 sequences. (Running on oeis4.)