A070056 - OEIS

%I #11 Sep 11 2017 04:40:21

%S 256,3327,28606,196301,1158554,6121871,29688844,134361100,574209267,

%T 2337788346,9128782573,34372098576,125327730017,444081743234,

%U 1533640995983,5174881667481,17096446731321,55402030270777,176377009761145,552397160169465,1704039417961465,5183132984363513,15559823619750905,46141145945628665

%N Number of Bottleneck-Monge matrices with 8 rows.

%C Bottleneck-Monge matrices are {0,1} matrices A in which, for every i<j and k<l, max(A[i,l],A[j,k]) <= max(A[i,k],A[j,l]).

%H Nathaniel Johnston, <a href="/A070056/b070056.txt">Table of n, a(n) for n = 1..400</a>

%F a(N) = a(8, N), where a(P, N) is defined recursively in A070050.

%F G.f.: x*(256 - 4609*x + 40669*x^2 - 232695*x^3 + 961183*x^4 - 3017869*x^5 + 7388387*x^6 - 14256058*x^7 + 21694227*x^8 - 25838259*x^9 + 23693517*x^10 - 16267523*x^11 + 7986763*x^12 - 2589705*x^13 + 474491*x^14 - 32768*x^15) / ((1 - x)*(1 - 2*x)^15) (conjectured). - _Colin Barker_, Sep 10 2017

%Y Cf. A070050, A070051, A070052, A070053, A070054, A070055, A070057.

%K nonn

%O 1,1

%A Pascal Prea (pascal.prea(AT)lim.univ-mrs.fr), Apr 18 2002

%E a(10)-a(24) from _Nathaniel Johnston_, Apr 13 2011