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A223770 T(n,k)=Number of nXk 0..1 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing.

%I A223770 #6 Jul 23 2025 04:29:49
%S A223770 2,4,4,7,12,7,11,28,28,11,16,56,71,56,16,22,101,155,155,101,22,29,169,
%T A223770 317,361,317,169,29,37,267,607,782,782,607,267,37,46,403,1097,1601,
%U A223770 1748,1601,1097,403,46,56,586,1887,3141,3699,3699,3141,1887,586,56,67,826
%N A223770 T(n,k)=Number of nXk 0..1 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing.
%C A223770 Table starts
%C A223770 ..2...4....7....11....16.....22.....29.....37......46......56......67.......79
%C A223770 ..4..12...28....56...101....169....267....403.....586.....826....1134.....1522
%C A223770 ..7..28...71...155...317....607...1097...1887....3112....4950....7631....11447
%C A223770 .11..56..155...361...782...1601...3141...5907...10678...18618...31422....51505
%C A223770 .16.101..317...782..1748...3699...7564..14980...28778...53619...96979...170525
%C A223770 .22.169..607..1601..3699...8007..16742..34096...67890..132115..251110...465910
%C A223770 .29.267.1097..3141..7564..16742..35513..73427..149053..297518..583860..1125118
%C A223770 .37.403.1887..5907.14980..34096..73427.153450..314878..637213.1273700..2513629
%C A223770 .46.586.3112.10678.28778..67890.149053.314878..651075.1327905.2680691..5361746
%C A223770 .56.826.4950.18618.53619.132115.297518.637213.1327905.2723829.5530333.11141645
%H A223770 R. H. Hardin, <a href="/A223770/b223770.txt">Table of n, a(n) for n = 1..363</a>
%F A223770 Empirical: columns 1..7 are polynomials of degree 2*k for n>0,0,2,4,6,8,10
%e A223770 Some solutions for n=3 k=4
%e A223770 ..0..0..0..1....0..0..0..0....1..1..0..0....0..0..1..0....0..0..1..0
%e A223770 ..0..0..0..1....1..0..0..0....1..1..1..0....1..1..1..1....0..1..1..1
%e A223770 ..0..0..0..1....1..1..1..1....1..1..1..1....0..1..1..1....0..1..1..1
%Y A223770 Column 1 is A000124
%K A223770 nonn,tabl
%O A223770 1,1
%A A223770 _R. H. Hardin_ Mar 27 2013