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 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) 5
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified July 14 11:30 EDT 2024. Contains 374318 sequences. (Running on oeis4.)