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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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2
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1, 1, 42, 9529, 6421892, 9652612995, 27361464052486, 131032872291901741, 980985180215656298952, 10837828798232467724499511, 168999527708576706854487574250, 3590193461689323277342585899536097
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| I. A. Blake and A. G. Konheim, Big buckets are (are not) better!, J. ACM, 24 (1977), 591-606.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| Reference gives recurrences.
Reference gives recurrences (see Mathematica code).
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MATHEMATICA
| 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
| Cf. A006698, A006700.
Sequence in context: A005791 A167668 A153471 * A109817 A159417 A095423
Adjacent sequences: A006696 A006697 A006698 * A006700 A006701 A006702
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms and better description from Reiner Martin (reinermartin(AT)hotmail.com), Feb 08 2002
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