A005340 Number of ways in which n identical balls can be distributed among 7 boxes in a row such that each pair of adjacent boxes contains at least 4 balls. (Formerly M4903)

1, 13, 76, 295, 889, 2188, 4652, 8891, 15686, 26011, 41056, 62251, 91291, 130162, 181168, 246959, 330560, 435401, 565348, 724735, 918397, 1151704, 1430596, 1761619, 2151962, 2609495, 3142808, 3761251, 4474975, 5294974, 6233128

Offset

12,2

References

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 12..1000

D. R. Breach, Letter to N. J. A. Sloane, Jun 1980

Philippe Flajolet, Balls and Urns, etc., A problem in submarine detection (solution to problem 68-16).

M. Hayes (proposer) and D. R. Breach (solver), A combinatorial problem, Problem 68-16, SIAM Rev. 12 (1970), 294-297.

Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

Formula

G.f.: x^12*(1 + 6*x + 6*x^2 + x^3 - 66*x^5 + 74*x^6 - 21*x^7)/(1-x)^7. - Vladeta Jovovic, Apr 13 2008

Mathematica

f[x_] := x^12*(1 + 6*x + 6*x^2 + x^3 - 66*x^5 + 74*x^6 - 21*x^7)/(1-x)^7; Drop[ CoefficientList[ Series[f[x], {x, 0, 42}], x], 12] (* Jean-François Alcover, Oct 05 2011, after Vladeta Jovovic *)

Crossrefs

Cf. A005337, A005338, A005339.

Sequence in context: A073544 A051361 A114070 * A114244 A050485 A034265

Adjacent sequences: A005337 A005338 A005339 * A005341 A005342 A005343

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vladeta Jovovic, Apr 13 2008

Name clarified by Alois P. Heinz, Oct 02 2017

Status

approved