A005338 Number of ways in which n identical balls can be distributed among 5 boxes in a row such that each pair of adjacent boxes contains at least 4 balls. (Formerly M4508)

1, 8, 31, 85, 190, 360, 610, 956, 1415, 2005, 2745, 3655, 4756, 6070, 7620, 9430, 11525, 13931, 16675, 19785, 23290, 27220, 31606, 36480, 41875, 47825, 54365, 61531, 69360, 77890, 87160, 97210, 108081, 119815, 132455, 146045, 160630

Offset

8,2

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 = 8..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 (5,-10,10,-5,1).

Formula

G.f.: x^8*(1 + 3*x + x^2 - 11*x^5 + 7*x^6)/(1 - x)^5. - Vladeta Jovovic, Apr 13 2008

a(n) = (n^4 + 10*n^3 - 445*n^2 + 2690*n - 1656)/24 for n > 9. - Colin Barker, May 10 2012

Mathematica

f[x_] := x^8*(1 + 3*x + x^2 - 11*x^5 + 7*x^6)/(1 - x)^5; Drop[ CoefficientList[ Series[f[x], {x, 0, 44}], x], 8] (* Jean-François Alcover, Oct 05 2011, after Vladeta Jovovic *)
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 8, 31, 85, 190, 360, 610}, 40] (* Harvey P. Dale, Aug 26 2019 *)

Prog

(Magma) I:=[1, 8, 31, 85, 190, 360, 610]; [n le 7 select I[n] else 5*Self(n-1)-10*Self(n-2)+10*Self(n-3)-5*Self(n-4)+Self(n-5): n in [1..40]]; // Vincenzo Librandi, May 11 2012

Crossrefs

Cf. A005337, A005339, A005340.

Sequence in context: A115004 A303522 A299261 * A006322 A319906 A212064

Adjacent sequences: A005335 A005336 A005337 * A005339 A005340 A005341

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Corrected and extended by Vladeta Jovovic, Apr 13 2008

Name clarified by Alois P. Heinz, Oct 02 2017

Status

approved