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A224038 T(n,k)=Number of nXk 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

%I A224038 #6 Jul 23 2025 04:56:08
%S A224038 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,
%T A224038 298,377,128,9,43,119,252,488,848,987,256,10,53,161,363,734,1422,2419,
%U A224038 2584,512,11,64,212,508,1064,2149,4160,6908,6765,1024,12,76,273,695,1505,3107
%N A224038 T(n,k)=Number of nXk 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.
%C A224038 Table starts
%C A224038 ....2.....3.....4......5......6......7......8......9.....10.....11......12
%C A224038 ....4.....8....13.....19.....26.....34.....43.....53.....64.....76......89
%C A224038 ....8....21....37.....58.....85....119....161....212....273....345.....429
%C A224038 ...16....55...105....168....252....363....508....695....933...1232....1603
%C A224038 ...32...144...298....488....734...1064...1505...2091...2864...3875....5185
%C A224038 ...64...377...848...1422...2149...3107...4395...6124...8439..11527...15626
%C A224038 ..128...987..2419...4160...6321...9125..12856..17875..24623..33686...45837
%C A224038 ..256..2584..6908..12214..18673..26928..37808..52356..71923..98238..133616
%C A224038 ..512..6765.19737..35960..55373..79800.111683.154076.210890.287271..389967
%C A224038 .1024.17711.56401.106072.164729.237348.331170.455195.620860.843084.1141689
%H A224038 R. H. Hardin, <a href="/A224038/b224038.txt">Table of n, a(n) for n = 1..1012</a>
%F A224038 Empirical: columns k=1..7 have recurrences of order 1,2,5,7,9,11,13 for n>0,0,0,10,13,16
%F A224038 Empirical: rows n=1..7 are polynomials of degree n for k>0,0,1,2,3,4,5
%e A224038 Some solutions for n=3 k=4
%e A224038 ..0..0..0..1....1..1..1..1....0..0..0..1....0..0..0..1....0..0..0..1
%e A224038 ..0..1..1..1....1..1..1..1....1..1..1..1....0..0..0..0....0..1..1..1
%e A224038 ..0..0..1..1....0..1..1..1....1..1..1..1....0..0..0..0....1..1..1..1
%Y A224038 Column 1 is A000079
%Y A224038 Column 2 is A001906(n+1)
%Y A224038 Row 1 is A000027(n+1)
%Y A224038 Row 2 is A034856(n+1)
%K A224038 nonn,tabl
%O A224038 1,1
%A A224038 _R. H. Hardin_ Mar 30 2013