0,4

Differences of 0. Labeled ordered partitions into 3 parts.

Number of surjections from an n-element set onto a three-element set, with n >= 3. - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Dec 15 2007

Let P(A) be the power set of an n-element set A and R be a relation on P(A) such that for all x, y of P(A), xRy if either 0) x is not a subset of y and y is not a subset of x and x and y are disjoint, or 1) x is a proper subset of y or y is a proper subset of x and x and y are intersecting. Then a(n+1) = |R|. [From Ross La Haye (rlahaye(AT)new.rr.com), Mar 19 2009]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

H. T. Davis, Tables of the Mathematical Functions. Vols. 1 and 2, 2nd ed., 1963, Vol. 3 (with V. J. Fisher), 1962; Principia Press of Trinity Univ., San Antonio, TX, Vol. 2, p. 212.

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 33.

J. F. Steffensen, Interpolation, 2nd ed., Chelsea, NY, 1950, see p. 54.

A. H. Voigt, Theorie der Zahlenreihen und der Reihengleichungen, Goschen, Leipzig, 1911, p. 31.

Ross La Haye, Binary Relations on the Power Set of an n-Element Set, Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.6. [From Ross La Haye (rlahaye(AT)new.rr.com), Mar 19 2009]

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

A. H. Voigt, Theorie der Zahlenreihen und der Reihengleichungen, Leipzig, 1911.

3!*S(n, 3). E.g.f.: (e^x-1)^3.

For n>=3: a(n+1)=3*a(n)+3*[(2^n)-2]=3*a(n)+3*A000918(n) [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Feb 27 2009]

G.f.:(-1-11*x^2+6*x)/((x-1)*(3*x-1)*(2*x-1)) [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009]

with (combstruct):ZL:=[S, {S=Sequence(U, card=r), U=Set(Z, card>=1)}, labeled]: seq(count(subs(r=3, ZL), size=m), m=0..25); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 09 2007

A001117:=-6/(z-1)/(3*z-1)/(2*z-1); [Conjectured by S. Plouffe in his 1992 dissertation. Gives sequence except for three leading terms.]

Cf. A000919, A001118, A019538.

Sequence in context: A056375 A018214 A056268 this_sequence A055404 A132165 A074444

Adjacent sequences: A001114 A001115 A001116 this_sequence A001118 A001119 A001120

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).

Extended with formula and alternate description by Christian G. Bower (bowerc(AT)usa.net), Aug 15 1998.

Simpler description from Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Apr 07 2001