A224038 T(n,k)=Number of nXk 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing

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

R. H. Hardin, Table of n, a(n) for n = 1..1012

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

Adjacent sequences: A224035 A224036 A224037 * A224039 A224040 A224041

Keyword

nonn,tabl

Author

R. H. Hardin Mar 30 2013

Status

approved