|
%I #11 Sep 11 2017 04:40:29
%S 512,7935,77950,597725,3887592,22418665,117789230,574209267,
%T 2630933289,11438763414,47540271657,189960445332,733160014779,
%U 2743585958976,9986068392201,35447227965486,122988982790340,417920043272208,1393150860920936,4562718944632792,14700625316815800,46648299847265144,145938710212960504
%N Number of Bottleneck-Monge matrices with 9 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="/A070057/b070057.txt">Table of n, a(n) for n = 1..400</a>
%F a(N) = a(9, N), where a(P, N) is defined recursively in A070050.
%F G.f.: x*(512 - 9985*x + 96161*x^2 - 607903*x^3 + 2821517*x^4 - 10164757*x^5 + 29260931*x^6 - 68263237*x^7 + 129682732*x^8 - 200278047*x^9 + 249653465*x^10 - 247990203*x^11 + 192418577*x^12 - 113113161*x^13 + 48011519*x^14 - 13562349*x^15 + 2175308*x^16 - 131072*x^17) / ((1 - x)*(1 - 2*x)^17) (conjectured). - _Colin Barker_, Sep 10 2017
%Y Cf. A070050, A070051, A070052, A070053, A070054, A070055, A070056.
%K nonn
%O 1,1
%A Pascal Prea (pascal.prea(AT)lim.univ-mrs.fr), Apr 18 2002
%E a(9)-a(23) from _Nathaniel Johnston_, Apr 13 2011
|
