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A201384 T(n,k)=Number of nXk 0..1 arrays with rows and columns lexicographically nondecreasing and the instance counts of every value within one of each other.

%I A201384 #7 Jul 22 2025 16:13:07
%S A201384 2,1,1,2,3,2,1,4,4,1,2,7,19,7,2,1,9,27,27,9,1,2,13,115,121,115,13,2,1,
%T A201384 16,122,483,483,122,16,1,2,21,467,1751,7148,1751,467,21,2,1,25,433,
%U A201384 5694,24779,24779,5694,433,25,1,2,31,1461,16870,295813,326650,295813,16870
%N A201384 T(n,k)=Number of nXk 0..1 arrays with rows and columns lexicographically nondecreasing and the instance counts of every value within one of each other.
%C A201384 Table starts
%C A201384 .2..1....2......1........2..........1............2..............1
%C A201384 .1..3....4......7........9.........13...........16.............21
%C A201384 .2..4...19.....27......115........122..........467............433
%C A201384 .1..7...27....121......483.......1751.........5694..........16870
%C A201384 .2..9..115....483.....7148......24779.......295813.........804538
%C A201384 .1.13..122...1751....24779.....326650......3826202.......39589830
%C A201384 .2.16..467...5694...295813....3826202....175765510.....1819250859
%C A201384 .1.21..433..16870...804538...39589830...1819250859....74872992399
%C A201384 .2.25.1461..46014..7711613..364013320..65629320845..2730227923892
%C A201384 .1.31.1208.116842.17135660.3005372641.534428405524.88478723671041
%H A201384 R. H. Hardin, <a href="/A201384/b201384.txt">Table of n, a(n) for n = 1..219</a>
%e A201384 Some solutions for n=4 k=7
%e A201384 ..0..0..0..0..1..1..1....0..0..0..1..1..1..1....0..0..0..0..0..1..1
%e A201384 ..0..0..0..1..1..1..1....0..0..1..0..0..0..1....0..0..0..1..1..0..1
%e A201384 ..0..1..1..1..0..0..0....1..1..0..0..0..0..1....0..0..1..1..1..1..0
%e A201384 ..1..1..1..1..0..0..0....1..1..1..0..0..1..1....0..1..0..1..1..1..1
%Y A201384 Column 2 is A004652(n+1)
%K A201384 nonn,tabl
%O A201384 1,1
%A A201384 _R. H. Hardin_ Nov 30 2011