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%I M4903 #50 Jun 26 2023 14:51:46
%S 1,13,76,295,889,2188,4652,8891,15686,26011,41056,62251,91291,130162,
%T 181168,246959,330560,435401,565348,724735,918397,1151704,1430596,
%U 1761619,2151962,2609495,3142808,3761251,4474975,5294974,6233128
%N Number of ways in which n identical balls can be distributed among 7 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="/A005340/b005340.txt">Table of n, a(n) for n = 12..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 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7, -21, 35, -35, 21, -7, 1).
%F G.f.: x^12*(1 + 6*x + 6*x^2 + x^3 - 66*x^5 + 74*x^6 - 21*x^7)/(1-x)^7. - _Vladeta Jovovic_, Apr 13 2008
%t f[x_] := x^12*(1 + 6*x + 6*x^2 + x^3 - 66*x^5 + 74*x^6 - 21*x^7)/(1-x)^7; Drop[ CoefficientList[ Series[f[x], {x, 0, 42}], x], 12] (* _Jean-François Alcover_, Oct 05 2011, after _Vladeta Jovovic_ *)
%Y Cf. A005337, A005338, A005339.
%K nonn,easy
%O 12,2
%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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