A266362 - OEIS

%I #6 Jan 15 2022 21:21:07

%S 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 50,8,9,70,337,830,830,337,70,9,10,95,614,2278,3669,2278,614,95,10,11,

%U 125,1060,5752,14921,14921,5752,1060,125,11,12,161,1749,13525,55734,93085

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

%C Table starts

%C ..2...3....4.....5.......6........7..........8..........9.........10.........11

%C ..3...7...13....22......34.......50.........70.........95........125........161

%C ..4..13...35....82.....173......337........614.......1060.......1749.......2777

%C ..5..22...82...276.....830.....2278.......5752......13525......29864......62455

%C ..6..34..173...830....3669....14921......55734.....191916.....612871....1827072

%C ..7..50..337..2278...14921....93085.....541207....2909244...14424728...66153106

%C ..8..70..614..5752...55734...541207....5061414...44435916..361401441.2711340372

%C ..9..95.1060.13525..191916..2909244...44435916..654427939.9043864160

%C .10.125.1749.29864..612871.14424728..361401441.9043864160

%C .11.161.2777.62455.1827072.66153106.2711340372

%H R. H. Hardin, <a href="/A266362/b266362.txt">Table of n, a(n) for n = 1..143</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1) -a(n-2);

%F k=2: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5);

%F 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 Some solutions for n=4, k=4

%e ..0..0..0..1....0..0..0..1....0..0..1..1....0..0..1..1....0..0..0..0

%e ..0..0..1..1....0..0..0..1....0..1..0..1....0..1..1..1....0..0..0..1

%e ..0..1..1..0....1..1..1..0....0..1..1..1....1..1..0..1....0..1..1..0

%e ..1..0..0..1....1..1..1..0....1..1..1..0....1..1..1..1....0..1..1..1

%Y Column 1 is A000027(n+1).

%Y Column 2 is A002623.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 28 2015