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A223961 T(n,k)=Number of nXk 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

%I A223961 #6 Jul 23 2025 04:42:36
%S A223961 4,10,16,20,85,64,35,295,707,256,56,805,3471,5864,1024,84,1876,12311,
%T A223961 41006,48620,4096,120,3906,36028,176893,485714,403104,16384,165,7470,
%U A223961 92734,594286,2575955,5777663,3342081,65536,220,13365,217144,1718057
%N A223961 T(n,k)=Number of nXk 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.
%C A223961 Table starts
%C A223961 .......4.........10...........20............35.............56.............84
%C A223961 ......16.........85..........295...........805...........1876...........3906
%C A223961 ......64........707.........3471.........12311..........36028..........92734
%C A223961 .....256.......5864........41006........176893.........594286........1718057
%C A223961 ....1024......48620.......485714.......2575955........9779558.......30643468
%C A223961 ....4096.....403104......5777663......37844037......163752797......556027700
%C A223961 ...16384....3342081.....68892600.....559416917.....2772658693....10269723035
%C A223961 ...65536...27708726....822141033....8299429418....47273211674...191829887779
%C A223961 ..262144..229729153...9813968785..123370738379...809416786834..3609049327918
%C A223961 .1048576.1904652103.117159879996.1835707326614.13894273785956.68212899813271
%H A223961 R. H. Hardin, <a href="/A223961/b223961.txt">Table of n, a(n) for n = 1..287</a>
%F A223961 Empirical: columns k=1..5 have recurrences of order 1,4,13,34,63 for n>0,0,0,36,68
%F A223961 Empirical rows n=1..7 are polynomials of order 3*n for k>0,0,2,5,8,11,14
%e A223961 Some solutions for n=3 k=4
%e A223961 ..1..2..2..3....1..2..2..2....0..0..2..2....0..0..1..1....0..1..1..3
%e A223961 ..0..2..2..2....1..3..3..3....1..3..3..3....1..2..2..2....0..1..1..1
%e A223961 ..0..0..3..3....0..2..3..3....0..3..3..3....1..2..3..3....1..1..2..3
%Y A223961 Column 1 is A000302
%Y A223961 Column 2 is A038235
%Y A223961 Row 1 is A000292(n+1)
%K A223961 nonn,tabl
%O A223961 1,1
%A A223961 _R. H. Hardin_ Mar 29 2013