A070057 Number of Bottleneck-Monge matrices with 9 rows.

512, 7935, 77950, 597725, 3887592, 22418665, 117789230, 574209267, 2630933289, 11438763414, 47540271657, 189960445332, 733160014779, 2743585958976, 9986068392201, 35447227965486, 122988982790340, 417920043272208, 1393150860920936, 4562718944632792, 14700625316815800, 46648299847265144, 145938710212960504

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

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

Crossrefs

Cf. A070050, A070051, A070052, A070053, A070054, A070055, A070056.

Sequence in context: A255749 A251186 A257202 * A017619 A253928 A254887

Adjacent sequences: A070054 A070055 A070056 * A070058 A070059 A070060

Keyword

nonn

Author

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

Extensions

a(9)-a(23) from Nathaniel Johnston, Apr 13 2011

Status

approved