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 A057703 a(n) = n*(94 + 5*n + 25*n^2 - 5*n^3 + n^4)/120. 6
 0, 1, 3, 7, 15, 31, 62, 119, 218, 381, 637, 1023, 1585, 2379, 3472, 4943, 6884, 9401, 12615, 16663, 21699, 27895, 35442, 44551, 55454, 68405, 83681, 101583, 122437, 146595, 174436, 206367, 242824, 284273, 331211, 384167, 443703, 510415, 584934, 667927 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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? LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Michael Boardman, The Egg-Drop Numbers, Mathematics Magazine, 77 (2004), 368-372. [Parthasarathy Nambi, Sep 30 2009] Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1). FORMULA a(n) = n*(94 + 5*n + 25*n^2 - 5*n^3 + n^4)/120. a(n) = Sum_{j=1..5} binomial(n, j). - Labos Elemer G.f.: x*(1 - 3*x + 4*x^2 - 2*x^3 + x^4)/(1-x)^6. - Colin Barker, Apr 15 2012 E.g.f.: x*(120 + 60*x + 20*x^2 + 5*x^3 + x^4)*exp(x)/120. - G. C. Greubel, Jun 05 2019 MAPLE seq(sum(binomial(n, k), k=1..5), n=0..38); # Zerinvary Lajos, Dec 13 2007 MATHEMATICA LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 1, 3, 7, 15, 31}, 60] (* Vladimir Joseph Stephan Orlovsky, Feb 08 2012 *) PROG (PARI) vector(40, n, n--; n*(94+5*n+25*n^2-5*n^3+n^4)/120) \\ G. C. Greubel, Jun 05 2019 (MAGMA) [n*(94+5*n+25*n^2-5*n^3+n^4)/120: n in [0..40]]; // G. C. Greubel, Jun 05 2019 (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 (GAP) List([0..40], n-> n*(94+5*n+25*n^2-5*n^3+n^4)/120) # G. C. Greubel, Jun 05 2019 CROSSREFS Cf. A004006. Differences form A055795 + 1 = A000127. Sequence in context: A007574 A034480 A218281 * A006739 A119407 A224521 Adjacent sequences:  A057700 A057701 A057702 * A057704 A057705 A057706 KEYWORD nonn,easy AUTHOR Leonid Broukhis, Oct 24 2000 EXTENSIONS More terms and formula from James A. Sellers, Oct 25 2000 Name changed by G. C. Greubel, Jun 06 2019 STATUS approved

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Last modified November 12 09:29 EST 2019. Contains 329054 sequences. (Running on oeis4.)