A005339 Number of ways in which n identical balls can be distributed among 6 boxes in a row such that each pair of adjacent boxes contains at least 4 balls.

35, 154, 424, 930, 1775, 3080, 4985, 7650, 11256, 16006, 22126, 29866, 39501, 51332, 65687, 82922, 103422, 127602, 155908, 188818, 226843, 270528, 320453, 377234, 441524, 514014, 595434, 686554, 788185, 901180, 1026435, 1164890, 1317530

Offset: 12

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

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

Links

• 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 (6, -15, 20, -15, 6, -1).

Crossrefs

Cf. A005337, A005338, A005340.

Programs

Mathematica

Drop[CoefficientList[Series[x^12(35-56x+25x^2-4x^3+x^6)/(1-x)^6, {x,0, 60}], x],12] (* or *) Join[{35},LinearRecurrence[{6,-15,20,-15,6,-1},{154,424,930,1775,3080,4985},48]] (* Harvey P. Dale, Aug 12 2011 *)

Formula

G.f.: x^12*(35 - 56*x + 25*x^2 - 4*x^3 + x^6)/(1-x)^6. - Vladeta Jovovic, Apr 13 2008

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6), a(12)=35, a(13)=154, a(14)=424, a(15)=930, a(16)=1775, a(17)=3080, a(18)=4985. - Harvey P. Dale, Aug 12 2011

Extensions

More terms from Vladeta Jovovic, Apr 13 2008

Name clarified by Alois P. Heinz, Oct 02 2017