The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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