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
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