%I A115567
%S A115567 0,1,3,7,15,31,63,126,246,465,847,1485,2509,4095,6475,9948,14892,21777,
%T A115567 31179,43795,60459,82159,110055,145498,190050,245505,313911,397593,
%U A115567 499177,621615,768211,942648,1149016,1391841,1676115,2007327,2391495
%N A115567 C(n,6) + C(n,5) + C(n,4) + C(n,3) + C(n,2) + C(n,1).
%C A115567 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).
%C A115567 By analogy to A004006, A055795 and A057703, I presume that a(n) = Answer 
               to the question: if you have a tall building and 6 plates and you 
               need to find the highest story, a plate thrown from which does not 
               break, what is the number of stories you can handle given n tries?
%D A115567 Michael Boardman, "The Egg-Drop Numbers", Mathematics Magazine, 77 (2004), 
               368-372. [From Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Sep 
               30 2009]
%F A115567 a(n) = C(n,6) + C(n,5) + C(n,4) + C(n,3) + C(n,2) + C(n,1). a(n) = A000579(n) 
               + A000389(n) + A000332(n) + A000292(n) + A000217(n) + n. a(n) = A000579(n) 
               + A057703(n).
%p A115567 seq(sum(binomial(n,k),k=1..6),n=0..36); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Dec 13 2007
%o A115567 (Other) sage: [binomial(n,2)+binomial(n,4)+binomial(n,6) for n in xrange(1, 
               38)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 17 
               2009]
%o A115567 (Other) sage: [binomial(n,1)+binomial(n,3)+binomial(n,5)+binomial(n,2)+binomial(n,
               4)+binomial(n,6) for n in xrange(0, 37)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               May 17 2009]
%Y A115567 Cf. A000217, A000332, A000389, A000292, A000579, A004006, A055795, A057703.
%Y A115567 Sequence in context: A043734 A151359 A147596 this_sequence A043740 A116082 
               A043747
%Y A115567 Adjacent sequences: A115564 A115565 A115566 this_sequence A115568 A115569 
               A115570
%K A115567 easy,nonn
%O A115567 0,3
%A A115567 Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 12 2006