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.
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
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).
Programs
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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 *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,13,76,295,889,2188,4652,8891},40] (* Harvey P. Dale, Apr 03 2025 *)
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
Extensions
More terms from Vladeta Jovovic, Apr 13 2008
Name clarified by Alois P. Heinz, Oct 02 2017