cp's OEIS Frontend

A266362 T(n,k) = Number of n X k binary arrays with rows and columns lexicographically nondecreasing and row and column sums nondecreasing.

%I A266362 #6 Jan 15 2022 21:21:07
%S A266362 2,3,3,4,7,4,5,13,13,5,6,22,35,22,6,7,34,82,82,34,7,8,50,173,276,173,
%T A266362 50,8,9,70,337,830,830,337,70,9,10,95,614,2278,3669,2278,614,95,10,11,
%U A266362 125,1060,5752,14921,14921,5752,1060,125,11,12,161,1749,13525,55734,93085
%N A266362 T(n,k) = Number of n X k binary arrays with rows and columns lexicographically nondecreasing and row and column sums nondecreasing.
%C A266362 Table starts
%C A266362 ..2...3....4.....5.......6........7..........8..........9.........10.........11
%C A266362 ..3...7...13....22......34.......50.........70.........95........125........161
%C A266362 ..4..13...35....82.....173......337........614.......1060.......1749.......2777
%C A266362 ..5..22...82...276.....830.....2278.......5752......13525......29864......62455
%C A266362 ..6..34..173...830....3669....14921......55734.....191916.....612871....1827072
%C A266362 ..7..50..337..2278...14921....93085.....541207....2909244...14424728...66153106
%C A266362 ..8..70..614..5752...55734...541207....5061414...44435916..361401441.2711340372
%C A266362 ..9..95.1060.13525..191916..2909244...44435916..654427939.9043864160
%C A266362 .10.125.1749.29864..612871.14424728..361401441.9043864160
%C A266362 .11.161.2777.62455.1827072.66153106.2711340372
%H A266362 R. H. Hardin, <a href="/A266362/b266362.txt">Table of n, a(n) for n = 1..143</a>
%F A266362 Empirical for column k:
%F A266362 k=1: a(n) = 2*a(n-1) -a(n-2);
%F A266362 k=2: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5);
%F A266362 k=3: a(n) = 5*a(n-1) -9*a(n-2) +6*a(n-3) -6*a(n-7) +9*a(n-8) -5*a(n-9) +a(n-10).
%e A266362 Some solutions for n=4, k=4
%e A266362 ..0..0..0..1....0..0..0..1....0..0..1..1....0..0..1..1....0..0..0..0
%e A266362 ..0..0..1..1....0..0..0..1....0..1..0..1....0..1..1..1....0..0..0..1
%e A266362 ..0..1..1..0....1..1..1..0....0..1..1..1....1..1..0..1....0..1..1..0
%e A266362 ..1..0..0..1....1..1..1..0....1..1..1..0....1..1..1..1....0..1..1..1
%Y A266362 Column 1 is A000027(n+1).
%Y A266362 Column 2 is A002623.
%K A266362 nonn,tabl
%O A266362 1,1
%A A266362 _R. H. Hardin_, Dec 28 2015