A070056 Number of Bottleneck-Monge matrices with 8 rows.

256, 3327, 28606, 196301, 1158554, 6121871, 29688844, 134361100, 574209267, 2337788346, 9128782573, 34372098576, 125327730017, 444081743234, 1533640995983, 5174881667481, 17096446731321, 55402030270777, 176377009761145, 552397160169465, 1704039417961465, 5183132984363513, 15559823619750905, 46141145945628665

Offset

1,1

Comments

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]).

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..400

Formula

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

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

Crossrefs

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

Sequence in context: A236254 A236251 A344304 * A185575 A185933 A185572

Adjacent sequences: A070053 A070054 A070055 * A070057 A070058 A070059

Keyword

nonn

Author

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

Extensions

a(10)-a(24) from Nathaniel Johnston, Apr 13 2011

Status

approved