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Search: id:A006700
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| A006700 |
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T(n,3,1), where T(n,k,s) with 0<=s<n is the number of sequences a_1,...,a_(k*n+s) of integers 0,1,...,n such that the 'bumped' sequence b_1,...,b_(k*n+s) has exactly s n's, 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 M4038)
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+0
3
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| 1, 5, 393, 131473, 117316993, 219639324573, 745567087151089, 4160071323762705545, 35561839228620292884321, 441709871992325805279854773, 7649447738065395278958097645657
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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.
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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. A006698, A006699.
Sequence in context: A152438 A060506 A057633 this_sequence A079011 A128866 A075769
Adjacent sequences: A006697 A006698 A006699 this_sequence A006701 A006702 A006703
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms and better description from Reiner Martin (reinermartin(AT)hotmail.com), Feb 07 2002
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