A005337 Number of ways in which n identical balls can be distributed among 4 boxes in a row such that each pair of adjacent boxes contains at least 4 balls. (Formerly M4963)

15, 40, 76, 124, 185, 260, 350, 456, 579, 720, 880, 1060, 1261, 1484, 1730, 2000, 2295, 2616, 2964, 3340, 3745, 4180, 4646, 5144, 5675, 6240, 6840, 7476, 8149, 8860, 9610, 10400, 11231, 12104, 13020, 13980, 14985

Offset

8,1

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.

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

G.f.: x^8*(15 - 20*x + 6*x^2)/(1 - x)^4.

a(n) = (546 - 169*n + 6*n^2 + n^3)/6. [Colin Barker, Jul 08 2012]

Maple

A005337:=(15-20*z+6*z**2)/(z-1)**4; # Simon Plouffe in his 1992 dissertation

Mathematica

CoefficientList[Series[(15 - 20 x + 6 x^2)/(1 - x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Oct 14 2013 *)
LinearRecurrence[{4, -6, 4, -1}, {15, 40, 76, 124}, 50] (* Harvey P. Dale, May 11 2014 *)

Crossrefs

Cf. A005338, A005339, A005340. A column of A259975.

Sequence in context: A044473 A321491 A067724 * A160891 A223425 A175926

Adjacent sequences: A005334 A005335 A005336 * A005338 A005339 A005340

Keyword

nonn,easy

Author

N. J. A. Sloane, Simon Plouffe

Extensions

G.f. corrected by Colin Barker, Jul 08 2012

Name clarified by Alois P. Heinz, Oct 02 2017

Status

approved