A250813 - OEIS

%I #8 Nov 21 2018 06:13:47

%S 36,100,225,441,784,1296,2025,3025,4356,6084,8281,11025,14400,18496,

%T 23409,29241,36100,44100,53361,64009,76176,90000,105625,123201,142884,

%U 164836,189225,216225,246016,278784,314721,354025,396900,443556,494209

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

%H R. H. Hardin, <a href="/A250813/b250813.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/4)*n^4 + (5/2)*n^3 + (37/4)*n^2 + 15*n + 9.

%F Conjectures from _Colin Barker_, Nov 21 2018: (Start)

%F G.f.: x*(36 - 80*x + 85*x^2 - 44*x^3 + 9*x^4) / (1 - x)^5.

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

%F (End)

%e Some solutions for n=4:

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

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

%Y Row 1 of A250812.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 27 2014