A005337 - OEIS

%I M4963 #52 Apr 13 2022 13:25:17

%S 15,40,76,124,185,260,350,456,579,720,880,1060,1261,1484,1730,2000,

%T 2295,2616,2964,3340,3745,4180,4646,5144,5675,6240,6840,7476,8149,

%U 8860,9610,10400,11231,12104,13020,13980,14985

%N 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.

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

%H Vincenzo Librandi, <a href="/A005337/b005337.txt">Table of n, a(n) for n = 8..1000</a>

%H D. R. Breach, <a href="/A004120/a004120.pdf">Letter to N. J. A. Sloane, Jun 1980</a>

%H Philippe Flajolet, <a href="http://algo.inria.fr/libraries/autocomb/balls-html/balls.html">Balls and Urns, etc.</a>, A problem in submarine detection (solution to problem 68-16).

%H M. Hayes (proposer) and D. R. Breach (solver), <a href="https://doi.org/10.1137/1012060">A combinatorial problem, Problem 68-16</a>, SIAM Rev. 12 (1970), 294-297.

%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

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

%F a(n) = (546 - 169*n + 6*n^2 + n^3)/6. [_Colin Barker_, Jul 08 2012]

%p A005337:=(15-20*z+6*z**2)/(z-1)**4; # _Simon Plouffe_ in his 1992 dissertation

%t CoefficientList[Series[(15 - 20 x + 6 x^2)/(1 - x)^4, {x, 0, 40}], x] (* _Vincenzo Librandi_, Oct 14 2013 *)

%t LinearRecurrence[{4,-6,4,-1},{15,40,76,124},50] (* _Harvey P. Dale_, May 11 2014 *)

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

%K nonn,easy

%O 8,1

%A _N. J. A. Sloane_, _Simon Plouffe_

%E G.f. corrected by _Colin Barker_, Jul 08 2012

%E Name clarified by _Alois P. Heinz_, Oct 02 2017