A250902 - OEIS

%I #8 Nov 23 2018 08:52:49

%S 1333,4750,14196,39003,102789,265546,680504,1742387,4479925,11612686,

%T 30445732,80928947,218431629,598934874,1667663960,4709666459,

%U 13467918413,38924144238,113481270292,333163706923,983467807413,2915295816330

%N Number of (4+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

%H R. H. Hardin, <a href="/A250902/b250902.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*(1333 - 13912*x + 61001*x^2 - 147893*x^3 + 218694*x^4 - 204317*x^5 + 119174*x^6 - 39804*x^7 + 5832*x^8) /((1 - x)^5*(1 - 2*x)^3*(1 - 3*x)). - _Colin Barker_, Nov 23 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Row 4 of A250898.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 28 2014