login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A178759 Expansion of e.g.f. 3*x*exp(x)*(exp(x)-1)^2. 1
0, 0, 0, 18, 144, 750, 3240, 12642, 46368, 163350, 559800, 1881066, 6229872, 20406750, 66273480, 213759090, 685601856, 2188698150, 6959413080, 22053083514, 69672773520, 219535296750, 690106487400, 2164714299138, 6777100916064, 21179698653750, 66083277045240, 205880260458762 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(n) is the sum of the digits in ternary sequences of length n, in which each element of the alphabet, {0,1,2} appears at least once in the sequence.

Generally, the e.g.f. for such sum of n-ary sequences (taken on an alphabet of {0,1,2,...,n-1}) is binomial(n,2)*x*exp(x)*(exp(x)-1)^(n-1).

Cf. A058877 which is the sum of the digits in such binary sequences.

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index to sequences with linear recurrences with constant coefficients, signature (12,-58,144,-193,132,-36).

FORMULA

E.g.f.: 3*x*exp(x)*(exp(x)-1)^2.

a(n) = (3^n-3*2^n+3)*n. - Mark van Hoeij, May 13 2013

G.f.: 6*x^3*(11*x^2-12*x+3) / ((x-1)^2*(2*x-1)^2*(3*x-1)^2). - Colin Barker, Nov 30 2014

EXAMPLE

a(3)=18 because there are six length 3 sequences on {0,1,2} that contain at least one 0, at least one 1 and at least one 2: (0,1,2),(0,2,1),(1,0,2),(1,2,0),(2,0,1),(2,1,0).  The digits sum to 18.

MATHEMATICA

Range[0, 20]! CoefficientList[Series[3x Exp[x](Exp[x]-1)^2, {x, 0, 20}], x]

PROG

(PARI) x='x+O('x^66); concat([0, 0, 0], Vec(serlaplace(3*x*exp(x)*(exp(x)-1)^2))) \\ Joerg Arndt, May 13 2013

(PARI) concat([0, 0, 0], Vec(6*x^3*(11*x^2-12*x+3)/((x-1)^2*(2*x-1)^2*(3*x-1)^2) + O(x^100))) \\ Colin Barker, Nov 30 2014

CROSSREFS

Cf. A058877, A178756.

Sequence in context: A127408 A008452 A126900 * A036397 A247741 A224329

Adjacent sequences:  A178756 A178757 A178758 * A178760 A178761 A178762

KEYWORD

nonn,easy

AUTHOR

Geoffrey Critzer, Dec 26 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified December 22 21:10 EST 2014. Contains 252372 sequences.