This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A057703 #45 Jul 03 2025 10:52:13
%S A057703 0,1,3,7,15,31,62,119,218,381,637,1023,1585,2379,3472,4943,6884,9401,
%T A057703 12615,16663,21699,27895,35442,44551,55454,68405,83681,101583,122437,
%U A057703 146595,174436,206367,242824,284273,331211,384167,443703,510415,584934,667927
%N A057703 a(n) = n*(94 + 5*n + 25*n^2 - 5*n^3 + n^4)/120.
%C A057703 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?
%C A057703 Number of compositions with at most five parts and sum at most n. - _Beimar Naranjo_, Mar 12 2024
%H A057703 G. C. Greubel, <a href="/A057703/b057703.txt">Table of n, a(n) for n = 0..1000</a>
%H A057703 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 A057703 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A057703 a(n) = n*(94 + 5*n + 25*n^2 - 5*n^3 + n^4)/120.
%F A057703 a(n) = Sum_{j=1..5} binomial(n, j). - _Labos Elemer_
%F A057703 G.f.: x*(1 - 3*x + 4*x^2 - 2*x^3 + x^4)/(1-x)^6. - _Colin Barker_, Apr 15 2012
%F A057703 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 A057703 seq(sum(binomial(n,k),k=1..5),n=0..38); # _Zerinvary Lajos_, Dec 13 2007
%t A057703 LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 1, 3, 7, 15, 31}, 60] (* _Vladimir Joseph Stephan Orlovsky_, Feb 08 2012 *)
%o A057703 (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 A057703 (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 A057703 (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 A057703 (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 A057703 Cf. A004006.
%Y A057703 Differences form A055795 + 1 = A000127.
%K A057703 nonn,easy
%O A057703 0,3
%A A057703 _Leonid Broukhis_, Oct 24 2000
%E A057703 More terms and formula from _James Sellers_, Oct 25 2000
%E A057703 Name changed by _G. C. Greubel_, Jun 06 2019