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A224038
T(n,k)=Number of nXk 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing
12
2, 3, 4, 4, 8, 8, 5, 13, 21, 16, 6, 19, 37, 55, 32, 7, 26, 58, 105, 144, 64, 8, 34, 85, 168, 298, 377, 128, 9, 43, 119, 252, 488, 848, 987, 256, 10, 53, 161, 363, 734, 1422, 2419, 2584, 512, 11, 64, 212, 508, 1064, 2149, 4160, 6908, 6765, 1024, 12, 76, 273, 695, 1505, 3107
OFFSET
1,1
COMMENTS
Table starts
....2.....3.....4......5......6......7......8......9.....10.....11......12
....4.....8....13.....19.....26.....34.....43.....53.....64.....76......89
....8....21....37.....58.....85....119....161....212....273....345.....429
...16....55...105....168....252....363....508....695....933...1232....1603
...32...144...298....488....734...1064...1505...2091...2864...3875....5185
...64...377...848...1422...2149...3107...4395...6124...8439..11527...15626
..128...987..2419...4160...6321...9125..12856..17875..24623..33686...45837
..256..2584..6908..12214..18673..26928..37808..52356..71923..98238..133616
..512..6765.19737..35960..55373..79800.111683.154076.210890.287271..389967
.1024.17711.56401.106072.164729.237348.331170.455195.620860.843084.1141689
LINKS
FORMULA
Empirical: columns k=1..7 have recurrences of order 1,2,5,7,9,11,13 for n>0,0,0,10,13,16
Empirical: rows n=1..7 are polynomials of degree n for k>0,0,1,2,3,4,5
EXAMPLE
Some solutions for n=3 k=4
..0..0..0..1....1..1..1..1....0..0..0..1....0..0..0..1....0..0..0..1
..0..1..1..1....1..1..1..1....1..1..1..1....0..0..0..0....0..1..1..1
..0..0..1..1....0..1..1..1....1..1..1..1....0..0..0..0....1..1..1..1
CROSSREFS
Column 1 is A000079
Column 2 is A001906(n+1)
Row 1 is A000027(n+1)
Row 2 is A034856(n+1)
Sequence in context: A364674 A319079 A325329 * A344680 A330147 A241037
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Mar 30 2013
STATUS
approved