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%I M5245 #38 Mar 23 2021 21:26:59
%S 35,154,424,930,1775,3080,4985,7650,11256,16006,22126,29866,39501,
%T 51332,65687,82922,103422,127602,155908,188818,226843,270528,320453,
%U 377234,441524,514014,595434,686554,788185,901180,1026435,1164890,1317530
%N 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.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%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 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6, -15, 20, -15, 6, -1).
%F G.f.: x^12*(35 - 56*x + 25*x^2 - 4*x^3 + x^6)/(1-x)^6. - _Vladeta Jovovic_, Apr 13 2008
%F 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
%t 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 *)
%Y Cf. A005337, A005338, A005340.
%K nonn,easy
%O 12,1
%A _N. J. A. Sloane_
%E More terms from _Vladeta Jovovic_, Apr 13 2008
%E Name clarified by _Alois P. Heinz_, Oct 02 2017
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