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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.
(Formerly M5245)
4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

12,1

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=12..44.

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

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

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

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 *)

CROSSREFS

Cf. A005337, A005338, A005340.

Sequence in context: A048628 A048629 A133534 * A045614 A154074 A260867

Adjacent sequences:  A005336 A005337 A005338 * A005340 A005341 A005342

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

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Last modified June 19 17:16 EDT 2019. Contains 324222 sequences. (Running on oeis4.)