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A006700 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)
2
1, 5, 393, 131473, 117316993, 219639324573, 745567087151089, 4160071323762705545, 35561839228620292884321, 441709871992325805279854773, 7649447738065395278958097645657 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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..10.

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

FORMULA

Reference gives recurrences.

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, A006699.

Sequence in context: A302394 A057633 A193126 * A079011 A195502 A189307

Adjacent sequences:  A006697 A006698 A006699 * A006701 A006702 A006703

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms and better description from Reiner Martin (reinermartin(AT)hotmail.com), Feb 07 2002

STATUS

approved

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Last modified March 26 00:29 EDT 2019. Contains 321479 sequences. (Running on oeis4.)