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Search: id:A006699
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| A006699 |
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T(3,3n), 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 M5282)
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+0
3
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| 1, 1, 42, 9529, 6421892, 9652612995, 27361464052486, 131032872291901741, 980985180215656298952, 10837828798232467724499511, 168999527708576706854487574250, 3590193461689323277342585899536097
(list; graph; listen)
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OFFSET
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0,3
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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.
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. A006698, A006700.
Sequence in context: A005791 A167668 A153471 this_sequence A109817 A159417 A095423
Adjacent sequences: A006696 A006697 A006698 this_sequence A006700 A006701 A006702
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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 08 2002
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