login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A258554 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock ne-sw antidiagonal difference nondecreasing horizontally and nw+se diagonal sum nondecreasing vertically 15
16, 44, 44, 104, 112, 104, 228, 210, 296, 228, 480, 344, 598, 652, 480, 988, 506, 985, 1244, 1329, 988, 2008, 683, 1403, 1891, 2384, 2530, 2008, 4052, 894, 1917, 2509, 3754, 3980, 4667, 4052, 8144, 1140, 2542, 3314, 5070, 6196, 6348, 8419, 8144, 16332, 1421 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

....16....44...104...228...480...988..2008..4052..8144..16332..32712..65476

....44...112...210...344...506...683...894..1140..1421...1725...2071...2460

...104...296...598...985..1403..1917..2542..3222..3940...4767...5718...6737

...228...652..1244..1891..2509..3314..4313..5356..6331...7470...8820..10231

...480..1329..2384..3754..5070..6662..8612.10720.12831..15045..17532..20200

...988..2530..3980..6196..8339.10854.13833.17058.20414..23858..27446..31237

..2008..4667..6348..9688.12940.16942.21653.26628.31806..37351..43158..49004

..4052..8419..9567.14216.18630.24300.31254.38451.45713..53599..62205..70891

..8144.14932.13847.20285.26240.33844.43655.54137.64507..75625..87878.100660

.16332.26184.19227.27687.35386.45166.57928.71823.85853.100830.116939.133789

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..8053

FORMULA

Empirical for column k:

k=1: a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3)

k=2: a(n) = 4*a(n-1) -5*a(n-2) +a(n-3) +3*a(n-4) -4*a(n-5) +2*a(n-6) +2*a(n-7) -3*a(n-8) +a(n-9) for n>11

k=3: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -4*a(n-5) +6*a(n-6) -4*a(n-7) +a(n-8) for n>11

k=4: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -4*a(n-5) +6*a(n-6) -4*a(n-7) +a(n-8) for n>12

k=5: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -4*a(n-5) +6*a(n-6) -4*a(n-7) +a(n-8) for n>13

k=6: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -4*a(n-5) +6*a(n-6) -4*a(n-7) +a(n-8) for n>14

k=7: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -4*a(n-5) +6*a(n-6) -4*a(n-7) +a(n-8) for n>15

Empirical for row n:

n=1: a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3)

n=2: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +a(n-4) -3*a(n-5) +3*a(n-6) -a(n-7) for n>10

n=3: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +a(n-4) -3*a(n-5) +3*a(n-6) -a(n-7) for n>10

n=4: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +a(n-4) -3*a(n-5) +3*a(n-6) -a(n-7) for n>11

n=5: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +a(n-4) -3*a(n-5) +3*a(n-6) -a(n-7) for n>12

n=6: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +a(n-4) -3*a(n-5) +3*a(n-6) -a(n-7) for n>13

n=7: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +a(n-4) -3*a(n-5) +3*a(n-6) -a(n-7) for n>14

EXAMPLE

Some solutions for n=4 k=4

..1..0..0..0..1....0..0..0..0..1....1..0..0..0..0....0..0..0..0..0

..1..0..0..0..1....0..0..0..0..0....1..0..0..0..0....1..0..0..0..0

..1..0..0..0..1....1..0..0..0..0....0..0..0..0..0....0..0..0..0..0

..1..0..0..1..1....1..1..1..1..1....1..1..0..0..0....1..1..1..1..1

..1..1..1..1..1....1..1..1..1..0....1..0..0..0..0....0..0..0..0..0

CROSSREFS

Sequence in context: A316636 A187721 A253397 * A253326 A204039 A235413

Adjacent sequences:  A258551 A258552 A258553 * A258555 A258556 A258557

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jun 03 2015

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)