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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
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 30 2014
STATUS
approved