A006698 T(2,2n), 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 M4813)

1, 1, 11, 378, 27213, 3378680, 645216039, 175804806912, 64820487788537, 31093204323279744, 18824085922156535715, 14040767751007803601664, 12652731866917353207799557, 13553071929305974778937888768

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..13.

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. A006699, A006700.

Sequence in context: A333466 A018893 A051862 * A348353 A048431 A286914

Adjacent sequences: A006695 A006696 A006697 * A006699 A006700 A006701

Keyword

nonn,easy

Author

N. J. A. Sloane.

Extensions

More terms and better description from Reiner Martin, Feb 08 2002

Status

approved