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)

1, 5, 393, 131473, 117316993, 219639324573, 745567087151089, 4160071323762705545, 35561839228620292884321, 441709871992325805279854773, 7649447738065395278958097645657

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, Feb 07 2002

Status

approved