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A224158 T(n,k)=Number of nXk 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

%I A224158 #6 Jul 23 2025 05:01:23
%S A224158 2,4,4,7,12,8,11,28,36,16,16,56,89,108,32,22,101,187,281,324,64,29,
%T A224158 169,373,574,900,972,128,37,267,702,1156,1783,2935,2916,256,46,403,
%U A224158 1252,2271,3469,5657,9681,8748,512,56,586,2130,4339,6786,10562,18408,32020,26244
%N A224158 T(n,k)=Number of nXk 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.
%C A224158 Table starts
%C A224158 ....2.....4......7.....11......16......22......29......37.......46.......56
%C A224158 ....4....12.....28.....56.....101.....169.....267.....403......586......826
%C A224158 ....8....36.....89....187.....373.....702....1252....2130.....3479.....5486
%C A224158 ...16...108....281....574....1156....2271....4339....8008....14257....24519
%C A224158 ...32...324....900...1783....3469....6786...13283...25624....48339....88755
%C A224158 ...64...972...2935...5657...10562...20065...39037...76393...148637...284937
%C A224158 ..128..2916...9681..18408...32910...60214..114537..222841...437497...857104
%C A224158 ..256..8748..32020..61140..105020..184233..340134..650819..1271950..2506424
%C A224158 ..512.26244.105937.205390..342575..575410.1025559.1918648..3705824..7278086
%C A224158 .1024.78732.350311.694018.1136503.1833641.3143071.5721195.10873402.21181267
%H A224158 R. H. Hardin, <a href="/A224158/b224158.txt">Table of n, a(n) for n = 1..797</a>
%F A224158 Empirical: columns k=1..7 have recurrences of order 1,1,9,13,20,24,33 for n>0,0,0,14,22,27,37
%F A224158 Empirical: rows n=1..7 are polynomials of degree 2*n for k>0,0,2,4,6,8,10
%e A224158 Some solutions for n=3 k=4
%e A224158 ..0..0..0..0....1..1..0..0....0..0..1..0....0..1..1..0....0..0..1..0
%e A224158 ..0..0..0..0....1..0..0..0....1..1..0..0....1..1..1..1....1..1..1..0
%e A224158 ..0..0..1..0....0..0..0..0....1..1..1..0....1..1..1..1....1..1..1..1
%Y A224158 Column 1 is A000079
%Y A224158 Column 2 is A003946
%Y A224158 Row 1 is A000124
%Y A224158 Row 2 is A223764
%K A224158 nonn,tabl
%O A224158 1,1
%A A224158 _R. H. Hardin_ Mar 31 2013