Revision History for A250731
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing all changes.
|
|
A250731
|
|
Number of (2+1) X (n+1) 0..1 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.
(history;
published version)
|
|
|
#7 by Alois P. Heinz at Fri Nov 16 10:57:24 EST 2018
|
|
|
|
#6 by Colin Barker at Fri Nov 16 10:52:17 EST 2018
|
|
|
|
#5 by Colin Barker at Fri Nov 16 10:51:32 EST 2018
|
| NAME
|
Number of (2+1)) X( (n+1) 0..1 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.
|
| COMMENTS
|
Row 2 of A250729
|
| FORMULA
|
Empirical: a(n) = 2*a(n-1) +) + 2*a(n-2) -) - 3*a(n-3) for n>4.
Empirical g.f.: x*(18 + 10*x - 18*x^2 - x^3) / ((1 - x)*(1 - x - 3*x^2)). - Colin Barker, Nov 16 2018
|
| EXAMPLE
|
Some solutions for n=4:
|
| CROSSREFS
|
Row 2 of A250729.
|
| STATUS
|
approved
editing
|
|
|
|
#4 by R. H. Hardin at Thu Nov 27 08:17:18 EST 2014
|
|
|
|
#3 by R. H. Hardin at Thu Nov 27 08:17:14 EST 2014
|
| LINKS
|
R. H. Hardin, <a href="/A250731/b250731.txt">Table of n, a(n) for n = 1..210</a>
|
|
|
|
#2 by R. H. Hardin at Thu Nov 27 08:16:56 EST 2014
|
| NAME
|
allocated for R. H. Hardin
Number of (2+1)X(n+1) 0..1 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
|
| DATA
|
18, 46, 110, 257, 596, 1376, 3173, 7310, 16838, 38777, 89300, 205640, 473549, 1090478, 2511134, 5782577, 13315988, 30663728, 70611701, 162602894, 374438006, 862246697, 1985560724, 4572300824, 10528983005, 24245885486, 55832834510
|
| OFFSET
|
1,1
|
| COMMENTS
|
Row 2 of A250729
|
| FORMULA
|
Empirical: a(n) = 2*a(n-1) +2*a(n-2) -3*a(n-3) for n>4
|
| EXAMPLE
|
Some solutions for n=4
..0..0..0..0..1....0..0..0..0..1....0..0..0..0..0....1..0..0..0..0
..0..1..0..0..1....0..1..0..0..1....0..0..0..0..0....0..1..0..0..1
..1..0..1..0..1....1..0..1..1..1....1..0..0..1..0....1..0..1..0..1
|
| KEYWORD
|
allocated
nonn
|
| AUTHOR
|
R. H. Hardin, Nov 27 2014
|
| STATUS
|
approved
editing
|
|
|
|
#1 by R. H. Hardin at Thu Nov 27 07:52:07 EST 2014
|
| NAME
|
allocated for R. H. Hardin
|
| KEYWORD
|
allocated
|
| STATUS
|
approved
|
|
|
|
|