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)

1, 1, 42, 9529, 6421892, 9652612995, 27361464052486, 131032872291901741, 980985180215656298952, 10837828798232467724499511, 168999527708576706854487574250, 3590193461689323277342585899536097

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, Feb 08 2002

Status

approved