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A224409 T(n,k)=Number of nXk 0..1 arrays with rows unimodal and antidiagonals nondecreasing.

%I A224409 #6 Jul 23 2025 05:09:41
%S A224409 2,4,4,7,12,8,11,28,36,16,16,56,100,108,32,22,101,228,358,324,64,29,
%T A224409 169,465,884,1288,972,128,37,267,879,1928,3436,4636,2916,256,46,403,
%U A224409 1568,3902,7812,13440,16684,8748,512,56,586,2668,7490,16420,31710,52700,60040
%N A224409 T(n,k)=Number of nXk 0..1 arrays with rows unimodal and antidiagonals nondecreasing.
%C A224409 Table starts
%C A224409 ....2.....4......7......11......16.......22.......29.......37........46
%C A224409 ....4....12.....28......56.....101......169......267......403.......586
%C A224409 ....8....36....100.....228.....465......879.....1568.....2668......4362
%C A224409 ...16...108....358.....884....1928.....3902.....7490....13784.....24467
%C A224409 ...32...324...1288....3436....7812....16420....32814....63202....118117
%C A224409 ...64...972...4636...13440...31710....68282...139638...275766....530583
%C A224409 ..128..2916..16684...52700..129402...284254...590254..1183226...2313915
%C A224409 ..256..8748..60040..206708..529846..1187830..2496332..5055858...9988498
%C A224409 ..512.26244.216064..810664.2172346..4979464.10583872.21606456..42996954
%C A224409 .1024.78732.777544.3178940.8908986.20913026.44986080.92478100.185065944
%H A224409 R. H. Hardin, <a href="/A224409/b224409.txt">Table of n, a(n) for n = 1..2445</a>
%F A224409 Empirical: columns k=1..7 have recurrences of order 1,1,3,4,5,6,7 for n>0,0,0,0,0,7,8
%F A224409 Empirical: rows n=1..7 are polynomials of degree 2*n for k>0,0,0,2,3,4,5
%e A224409 Some solutions for n=3 k=4
%e A224409 ..0..0..0..0....0..1..0..0....0..0..1..1....0..0..0..1....1..1..0..0
%e A224409 ..0..0..0..1....1..0..0..0....1..1..1..1....1..1..1..1....1..0..0..0
%e A224409 ..1..1..1..0....0..0..1..1....1..1..1..1....1..1..1..1....0..0..1..1
%Y A224409 Column 1 is A000079
%Y A224409 Column 2 is A003946
%Y A224409 Row 1 is A000124
%Y A224409 Row 2 is A223764
%K A224409 nonn,tabl
%O A224409 1,1
%A A224409 _R. H. Hardin_ Apr 05 2013