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A223644 T(n,k)=Number of nXk 0..1 arrays with rows, columns, diagonals and antidiagonals unimodal.

%I A223644 #6 Jul 23 2025 04:19:54
%S A223644 2,4,4,7,16,7,11,49,49,11,16,121,218,121,16,22,256,726,726,256,22,29,
%T A223644 484,2014,2962,2014,484,29,37,841,4904,9808,9808,4904,841,37,46,1369,
%U A223644 10797,28450,36947,28450,10797,1369,46,56,2116,21917,74599,120307,120307,74599
%N A223644 T(n,k)=Number of nXk 0..1 arrays with rows, columns, diagonals and antidiagonals unimodal.
%C A223644 Table starts
%C A223644 ..2....4.....7.....11......16.......22........29........37.........46
%C A223644 ..4...16....49....121.....256......484.......841......1369.......2116
%C A223644 ..7...49...218....726....2014.....4904.....10797.....21917......41601
%C A223644 .11..121...726...2962....9808....28450.....74599....179991.....404599
%C A223644 .16..256..2014...9808...36947...120307....354726....967582....2469396
%C A223644 .22..484..4904..28450..120307...428187...1370104...4063584...11337648
%C A223644 .29..841.10797..74599..354726..1370104...4682514..14767708...43862845
%C A223644 .37.1369.21917.179991..967582..4063584..14767708..49045356..152945545
%C A223644 .46.2116.41601.404599.2469396.11337648..43862845.152945545..497721760
%C A223644 .56.3136.74635.855417.5941152.29980136.124004457.454159399.1539486460
%H A223644 R. H. Hardin, <a href="/A223644/b223644.txt">Table of n, a(n) for n = 1..199</a>
%F A223644 Empirical: Columns 1..7 are polynomials of degree 2*k for n > 0,0,0,4,7,13,19
%e A223644 Some solutions for n=4 k=4
%e A223644 ..1..0..0..0....1..1..1..0....0..0..0..0....1..1..0..0....0..1..1..1
%e A223644 ..1..1..1..1....1..1..1..0....0..1..1..1....1..1..1..0....0..1..1..1
%e A223644 ..0..1..1..0....1..1..1..0....1..1..1..0....0..1..1..0....0..0..0..1
%e A223644 ..0..1..1..0....0..1..1..0....1..0..0..0....0..0..0..0....0..0..0..0
%Y A223644 Column 1 is A000124
%Y A223644 Column 2 is A086601
%K A223644 nonn,tabl
%O A223644 1,1
%A A223644 _R. H. Hardin_ Mar 24 2013