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Search: id:A006698
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| A006698 |
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T(2,2n), where T(k,m) is the number of sequences a_1,...,a_m of integers 0,1,...,n with n=floor(m/k) such that the 'bumped' sequence b_1,...,b_m has exactly k of each of 0,...,n-1, where b_i=a_i + j (mod n+1) with minimal j>=0 such that b_0,...,b_i contain at most k elements equal to b_i.
(Formerly M4813)
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+0
3
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| 1, 1, 11, 378, 27213, 3378680, 645216039, 175804806912, 64820487788537, 31093204323279744, 18824085922156535715, 14040767751007803601664, 12652731866917353207799557, 13553071929305974778937888768
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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I. A. Blake and A. G. Konheim, Big buckets are (are not) better!, J. ACM, 24 (1977), 591-606.
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FORMULA
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Reference gives recurrences.
Reference gives recurrences (see Mathematica code).
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MATHEMATICA
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T[k_, m_] := T[k, m] = If[m <= k, 1, Module[{n = Quotient[m, k]}, Sum[Binomial[m - 1, k i - 1] i T[k, k i - 1] T[k, m - k i], {i, 1, n}] + If[n k == m, 0, (n + 1)T[k, m - 1]]]]
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CROSSREFS
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Cf. A006699, A006700.
Sequence in context: A024149 A018893 A051862 this_sequence A048431 A052290 A055409
Adjacent sequences: A006695 A006696 A006697 this_sequence A006699 A006700 A006701
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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EXTENSIONS
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More terms and better description from Reiner Martin (reinermartin(AT)hotmail.com), Feb 08 2002
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