A235413 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with 2X2 subblock sums lexicographically nondecreasing rowwise and nonincreasing columnwise

16, 44, 44, 121, 172, 121, 286, 704, 704, 286, 676, 2302, 4256, 2302, 676, 1482, 7617, 20398, 20398, 7617, 1482, 3249, 21707, 98575, 150862, 98575, 21707, 3249, 6840, 62070, 397340, 1155953, 1155953, 397340, 62070, 6840, 14400, 160219, 1623115

Offset

1,1

Comments

Table starts

....16.....44......121........286...........676............1482

....44....172......704.......2302..........7617...........21707

...121....704.....4256......20398.........98575..........397340

...286...2302....20398.....150862.......1155953.........7379380

...676...7617....98575....1155953......13930916.......145005714

..1482..21707...397340....7379380.....145005714......2573684600

..3249..62070..1623115...48788187....1561049902.....48150637857

..6840.160219..5744912..273307984...14369333157....775525688659

.14400.413728.20612708.1578043496..137304769214..13190905086499

.29640.994013.65877470.7881635316.1126706100728.190687328015653

Links

R. H. Hardin, Table of n, a(n) for n = 1..143

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) -18*a(n-3) +17*a(n-4) +22*a(n-5) -36*a(n-6) +20*a(n-8) -8*a(n-9)

k=2: [order 31]

k=3: [order 73]

Example

Some solutions for n=4 k=4
..0..0..0..0..0....0..0..0..0..0....1..0..0..0..0....1..0..0..0..0
..1..0..1..0..1....1..1..0..0..0....1..1..1..0..1....1..0..1..0..0
..0..0..0..0..0....0..0..0..0..0....1..0..0..1..0....1..1..0..0..1
..1..1..1..1..1....1..1..0..0..0....1..1..1..0..1....1..1..1..0..1
..1..0..1..0..0....0..1..1..0..1....1..1..1..0..0....1..1..1..0..0

Crossrefs

Column 1 is A204032

Sequence in context: A258554 A253326 A204039 * A238255 A210375 A173560

Adjacent sequences: A235410 A235411 A235412 * A235414 A235415 A235416

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 10 2014

Status

approved