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

Author

R. H. Hardin Mar 30 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000079

Column 2 is A001906(n+1)

Row 1 is A000027(n+1)

Row 2 is A034856(n+1)

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