a sequence that needs extending

[N. J. A. Sloane]

This is a real sequence (as opposed to all the made-up
ones that have been submitted lately)

The reference is from 1994; i don't know if there
has been any progress since then
(although Dean Hickerson may know - he is cited several times
in the chapter where it appears).

It would be nice to have some more terms.

NJAS

%I A070214
%S A070214 1,2,5,8,11
%N A070214 Maximal number of occupied cells in all monotonic matrices of order n.
%C A070214 A monotonic matrix of order n is an n X n matrix in which cell contains 0 or 1 numbers from the set {1...n} subject to 3 conditions:
%C A070214 the filled-in entries in each row are strictly increasing;
%C A070214 the filled-in entries in each column are strictly decreasing;
%C A070214 for two filled-in cells with same entry, the one further right is higher (the positive slope condition).
%e A070214 a(3) >= 5 from this matrix:
%e A070214 2 - 3
%e A070214 - - 1
%e A070214 1 3 -
%e A070214 a(5) >= 11 from this matrix:
%e A070214 - - 4 - 5
%e A070214 4 - - 5 -
%e A070214 - - 1 2 3
%e A070214 3 5 - - -
%e A070214 1 2 - - -
%D A070214 S. K. Stein and S. Szabo, Algebra and Tiling, MAA Carus Monograph 25, 1994, page 95.
%O A070214 1,2
%K A070214 nonn,more
%F A070214 a(r*s) >= a(r)*a(s); if a(n) = n^e(n) then L := lim_{n -> infinity} e(n) exists and is in the range 1.513 <= L <= 2.
%A A070214 njas, Jul 24 2003
%E A070214 a(1)-a(5) computed by K. Joy.
%E A070214 Lower bounds for the next 5 entries (from Stein and Szabo) are 14, 19, 22, 28, 32.