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

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

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?

Number of compositions with at most five parts and sum at most n. - Beimar Naranjo, Mar 12 2024

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