OFFSET
0,3
COMMENTS
a(n) = n + T(n) + Tet(n) + Ptop(n) + 5-Simplex(n) + 6-Simplex(n), where T(n) = n-th triangular number A000217(n), Tet(n) = n-th tetrahedral number A000292(n), Ptop(n) = n-th pentatope number A000332(n), 5-Simplex(n) = n-th 5-simplex number A000389(n), 6-Simplex(n) = n-th 6-simplex number A000579(n).
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 (7,-21,35,-35,21,-7,1).
FORMULA
a(n) = C(n,6) + C(n,5) + C(n,4) + C(n,3) + C(n,2) + C(n,1).
G.f.: x*(1-x+x^2)*(1-3*x+3*x^2)/(1-x)^7. - Colin Barker, Mar 16 2012
From G. C. Greubel, Nov 25 2017: (Start)
a(n) = n*(n + 1)*(n^4 - 10*n^3 + 65*n^2 - 140*n + 444)/720.
E.g.f.: x*(720 + 360*x + 120*x^2 + 30*x^3 + 6*x^4 + x^5)*exp(x)/720. (End)
MAPLE
seq(sum(binomial(n, k), k=1..6), n=0..36); # Zerinvary Lajos, Dec 13 2007
MATHEMATICA
Table[n*(n + 1)*(n^4 - 10*n^3 + 65*n^2 - 140*n + 444)/720, {n, 0, 30}] (* G. C. Greubel, Nov 25 2017 *)
PROG
(Sage) [binomial(n, 2)+binomial(n, 4)+binomial(n, 6) for n in range(1, 38)] # Zerinvary Lajos, May 17 2009
(Sage) [binomial(n, 1)+binomial(n, 3)+binomial(n, 5)+binomial(n, 2)+binomial(n, 4)+binomial(n, 6) for n in range(0, 37)] # Zerinvary Lajos, May 17 2009
(PARI) for(n=0, 30, print1(n*(n + 1)*(n^4 - 10*n^3 + 65*n^2 - 140*n + 444)/720, ", ")) \\ G. C. Greubel, Nov 25 2017
(Magma) [n*(n + 1)*(n^4 - 10*n^3 + 65*n^2 - 140*n + 444)/720: n in [0..30]]; // G. C. Greubel, Nov 25 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Mar 12 2006
STATUS
approved