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A253326 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock sum nondecreasing horizontally, vertically and antidiagonally ne-to-sw 14
16, 44, 44, 121, 126, 121, 286, 373, 377, 286, 676, 1026, 1217, 848, 676, 1482, 2797, 3787, 2538, 2042, 1482, 3249, 6936, 11506, 7744, 6190, 4218, 3249, 6840, 17197, 31999, 23153, 19312, 11795, 9228, 6840, 14400, 39616, 86922, 66196, 58505, 34660 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

....16....44....121....286.....676....1482....3249.....6840....14400.....29640

....44...126....373...1026....2797....6936...17197....39616....91571....200800

...121...377...1217...3787...11506...31999...86922...217799...537127...1242718

...286...848...2538...7744...23153...66196..185672...487946..1267072...3085862

...676..2042...6190..19312...58505..173903..503944..1397185..3802746...9816070

..1482..4218..11795..34660...98741..283804..797324..2204476..6007384..15848356

..3249..9228..25659..74953..210417..600020.1660088..4590122.12462900..33364770

..6840.18482..48085.132376..349857..952108.2516513..6753250.17839818..47266844

.14400.38621..99653.271506..705922.1887609.4869987.12802392.32941939..85796433

.29640.76654.188562.490768.1217364.3123964.7734273.19644544.48847302.123940122

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..418

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 13]

k=3: [same order 13] for n>15

k=4: [same order 13] for n>19

k=5: [same order 13] for n>22

k=6: [same order 13] for n>23

k=7: [same order 13] for n>26

Empirical for row n:

n=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)

n=2: [order 21]

n=3: [order 39]

n=4: [order 45]

n=5: [order 63]

n=6: [order 65]

n=7: [order 87]

EXAMPLE

Some solutions for n=4 k=4

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

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

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

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

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

CROSSREFS

Column 1 and row 1 are A204032

Sequence in context: A187721 A253397 A258554 * A204039 A235413 A238255

Adjacent sequences:  A253323 A253324 A253325 * A253327 A253328 A253329

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Dec 30 2014

STATUS

approved

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Last modified May 25 10:05 EDT 2022. Contains 354066 sequences. (Running on oeis4.)