0,3

Answer to the question: if you have a tall building and 4 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?

If Y is a 2-subset of an n-set X then, for n>=4, a(n-3) is the number of 4-subsets of X which have no exactly one element in common with Y. - Milan R. Janjic (agnus(AT)blic.net), Dec 28 2007

Milan Janjic, Two Enumerative Functions

Alexsandar Petojevic, The Function vM_m(s; a; z) and Some Well-Known Sequences, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.7

Differences give A000127. Also a(1) = 1; a(n) = a(n-1) + 1 + A004006(n-1).

a(n) = C(n, 1) + C(n, 2) + C(n, 3) + C(n, 4) - James Sellers, Mar 16 2002

Row sums of triangle A134394. Also, binomial transform of [1, 2, 2, 2, 1, 0, 0, 0,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 23 2007

O.g.f.: -x^2(1-2x+2x^2)/(x-1)^5. a(n)=A000332(n)+A000217(n-1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 13 2008

[seq(binomial(n, 4)+binomial(n, 2), n=1..50)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 24 2006

seq(sum(binomial(n, k), k=1..4), n=0..43); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 13 2007

T(2n+1, n), array T as in A055794. Cf. A004006, A000127.

Cf. A134394.

Sequence in context: A080011 A120538 A002545 this_sequence A058695 A023610 A062544

Adjacent sequences: A055792 A055793 A055794 this_sequence A055796 A055797 A055798

nonn,easy

Clark Kimberling (ck6(AT)evansville.edu), May 28 2000

Better description from Leonid A. Broukhis (leob(AT)mailcom.com), Oct 24 2000

Edited by Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 24 2006