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A006699 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)
2
1, 1, 42, 9529, 6421892, 9652612995, 27361464052486, 131032872291901741, 980985180215656298952, 10837828798232467724499511, 168999527708576706854487574250, 3590193461689323277342585899536097 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=0..11.

I. A. Blake and A. G. Konheim, Big buckets are (are not) better!, J. ACM, 24 (1977), 591-606.

FORMULA

Reference gives recurrences.

Reference gives recurrences (see Mathematica code).

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]]]]

CROSSREFS

Cf. A006698, A006700.

Sequence in context: A211908 A246621 A153471 * A303055 A226262 A109817

Adjacent sequences:  A006696 A006697 A006698 * A006700 A006701 A006702

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms and better description from Reiner Martin (reinermartin(AT)hotmail.com), Feb 08 2002

STATUS

approved

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Last modified March 20 21:49 EDT 2019. Contains 321352 sequences. (Running on oeis4.)