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A070050
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Number of Bottleneck-Monge matrices with 2 rows. In the formula below, P=2.
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8
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4, 12, 33, 87, 223, 559, 1375, 3327, 7935, 18687, 43519, 100351, 229375, 520191, 1171455, 2621439, 5832703, 12910591, 28442623, 62390271, 136314879, 296747007, 643825663, 1392508927, 3003121663, 6459228159, 13857980415, 29662117887, 63350767615
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| A Bottleneck-Monge matrix is a {0,1} matrix A in which, for every i<j and k<l, max(A[i,l],A[j,k]) <= max(A[i,k], A[j,l]).
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LINKS
| Nathaniel Johnston, Table of n, a(n) for n = 1..400
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FORMULA
| a(P, N) = 1 + sum_{n=1..N, p=1..P} (C(N, n) * C(P, p) * K(p, n)),
where:
C(i, j) = binomial(i,j),
K(p, n) = sum_{i=1..n} (T(p, n, i)),
T(1, n, 1) = 1,
T(1, n, i) = 0, for i>1,
T(p, n, i) = sum_{j=i..n, k=1..i} T(p-1, j, k).
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MAPLE
| A:=proc(P, N)return 1+add(add(binomial(N, n)*binomial(P, p)*K(p, n), p=1..P), n=1..N):end:
K:=proc(p, n)global k:if(not type(k[p, n], integer))then k[p, n]:=add(T(p, n, i), i=1..n):fi:return k[p, n]:end:
T:=proc(p, n, i)global t:if(not type(t[p, n, i], integer))then if(p=1 and i=1)then t[p, n, i]:=1:elif(p=1)then t[p, n, i]:=0:else t[p, n, i]:=add(add(T(p-1, j, k), k=1..i), j=i..n):fi:fi:return t[p, n, i]:end:
seq(A(2, n), n=1..20); ##Nathaniel Johnston, Apr 13 2011
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CROSSREFS
| Cf. A070051 (P=3), A070052 (P=4), A070053 (P=5), A070054 (P=6), A070055 (P=7), A070054 (P=8), A070057 (P=9).
Sequence in context: A066536 A168078 A104747 * A186025 A027941 A135254
Adjacent sequences: A070047 A070048 A070049 * A070051 A070052 A070053
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KEYWORD
| nonn,easy
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AUTHOR
| Pascal Prea (pascal.preq(AT)lim.univ-mrs.fr), Apr 18 2002
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EXTENSIONS
| Edited by N. J. A. Sloane, Jan 25 2011
a(10) - a(29) and corrected recurrence from Nathaniel Johnston (nathaniel(AT)nathanieljohnston.com), Apr 13 2011
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