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A057703 a(n) = n*(94 + 5*n + 25*n^2 - 5*n^3 + n^4)/120. 6

%I #35 Sep 08 2022 08:45:02

%S 0,1,3,7,15,31,62,119,218,381,637,1023,1585,2379,3472,4943,6884,9401,

%T 12615,16663,21699,27895,35442,44551,55454,68405,83681,101583,122437,

%U 146595,174436,206367,242824,284273,331211,384167,443703,510415,584934,667927

%N a(n) = n*(94 + 5*n + 25*n^2 - 5*n^3 + n^4)/120.

%C Previous name was: This sequence is the result of the question: If you have a tall building and 5 plates and you need to find the highest story from which a plate thrown does not break, what is the number of stories you can handle given n tries?

%H G. C. Greubel, <a href="/A057703/b057703.txt">Table of n, a(n) for n = 0..1000</a>

%H Michael Boardman, <a href="http://www.jstor.org/stable/3219201">The Egg-Drop Numbers</a>, Mathematics Magazine, 77 (2004), 368-372. [_Parthasarathy Nambi_, Sep 30 2009]

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F a(n) = n*(94 + 5*n + 25*n^2 - 5*n^3 + n^4)/120.

%F a(n) = Sum_{j=1..5} binomial(n, j). - _Labos Elemer_

%F G.f.: x*(1 - 3*x + 4*x^2 - 2*x^3 + x^4)/(1-x)^6. - _Colin Barker_, Apr 15 2012

%F E.g.f.: x*(120 + 60*x + 20*x^2 + 5*x^3 + x^4)*exp(x)/120. - _G. C. Greubel_, Jun 05 2019

%p seq(sum(binomial(n,k),k=1..5),n=0..38); # _Zerinvary Lajos_, Dec 13 2007

%t LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 1, 3, 7, 15, 31}, 60] (* _Vladimir Joseph Stephan Orlovsky_, Feb 08 2012 *)

%o (PARI) vector(40, n, n--; n*(94+5*n+25*n^2-5*n^3+n^4)/120) \\ _G. C. Greubel_, Jun 05 2019

%o (Magma) [n*(94+5*n+25*n^2-5*n^3+n^4)/120: n in [0..40]]; // _G. C. Greubel_, Jun 05 2019

%o (Sage) [n*(94+5*n+25*n^2-5*n^3+n^4)/120 for n in (0..40)] # _G. C. Greubel_, Jun 05 2019

%o (GAP) List([0..40], n-> n*(94+5*n+25*n^2-5*n^3+n^4)/120) # _G. C. Greubel_, Jun 05 2019

%Y Cf. A004006.

%Y Differences form A055795 + 1 = A000127.

%K nonn,easy

%O 0,3

%A _Leonid Broukhis_, Oct 24 2000

%E More terms and formula from _James A. Sellers_, Oct 25 2000

%E Name changed by _G. C. Greubel_, Jun 06 2019

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Last modified March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)