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A057703
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a(n) = n*(94 + 5*n + 25*n^2 - 5*n^3 + n^4)/120.
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6
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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
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OFFSET
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0,3
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COMMENTS
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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?
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LINKS
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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).
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FORMULA
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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
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MAPLE
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seq(sum(binomial(n, k), k=1..5), n=0..38); # Zerinvary Lajos, Dec 13 2007
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MATHEMATICA
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LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 1, 3, 7, 15, 31}, 60] (* Vladimir Joseph Stephan Orlovsky, Feb 08 2012 *)
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PROG
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(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
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CROSSREFS
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Cf. A004006.
Differences form A055795 + 1 = A000127.
Sequence in context: A007574 A034480 A218281 * A006739 A119407 A224521
Adjacent sequences: A057700 A057701 A057702 * A057704 A057705 A057706
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KEYWORD
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nonn,easy
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AUTHOR
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Leonid Broukhis, Oct 24 2000
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EXTENSIONS
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More terms and formula from James A. Sellers, Oct 25 2000
Name changed by G. C. Greubel, Jun 06 2019
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STATUS
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approved
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