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

Author

Leonid Broukhis, Oct 24 2000

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A004006.

Differences form A055795 + 1 = A000127.

Programs

GAP

List([0..40], 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

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 *)

PARI

vector(40, n, n--; n*(94+5*n+25*n^2-5*n^3+n^4)/120) \\ 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

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

Extensions

More terms and formula from James Sellers, Oct 25 2000

Name changed by G. C. Greubel, Jun 06 2019