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 A250816 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 min(x(i,j),x(i-1,j)) in the j direction. 1

%I #8 Nov 21 2018 06:14:07

%S 1389,4321,10233,20631,37333,62469,98481,148123,214461,300873,411049,

%T 548991,719013,925741,1174113,1469379,1817101,2223153,2693721,3235303,

%U 3854709,4559061,5355793,6252651,7257693,8379289,9626121,11007183

%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 min(x(i,j),x(i-1,j)) in the j direction.

%H R. H. Hardin, <a href="/A250816/b250816.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 13*n^4 + 121*n^3 + 439*n^2 + 573*n + 243.

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

%F G.f.: x*(1389 - 2624*x + 2518*x^2 - 1214*x^3 + 243*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 ..0..0..0..0..0....2..2..1..1..0....2..2..2..1..0....2..2..2..2..1

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

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

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

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

%Y Row 4 of A250812.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 27 2014

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Last modified June 14 05:27 EDT 2024. Contains 373393 sequences. (Running on oeis4.)