0,3

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).

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?

Michael Boardman, "The Egg-Drop Numbers", Mathematics Magazine, 77 (2004), 368-372. [From Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Sep 30 2009]

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).

seq(sum(binomial(n, k), k=1..6), n=0..36); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 13 2007

(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]

(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]

Cf. A000217, A000332, A000389, A000292, A000579, A004006, A055795, A057703.

Sequence in context: A043734 A151359 A147596 this_sequence A043740 A116082 A043747

Adjacent sequences: A115564 A115565 A115566 this_sequence A115568 A115569 A115570

easy,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 12 2006