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

 

Logo

Many excellent designs for a new banner were submitted. We will use the best of them in rotation.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A080855 (9*n^2-3*n+2)/2. 7
1, 4, 16, 37, 67, 106, 154, 211, 277, 352, 436, 529, 631, 742, 862, 991, 1129, 1276, 1432, 1597, 1771, 1954, 2146, 2347, 2557, 2776, 3004, 3241, 3487, 3742, 4006, 4279, 4561, 4852, 5152, 5461, 5779, 6106, 6442, 6787, 7141, 7504, 7876, 8257, 8647, 9046 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The old definition of this sequence was "Generalized polygonal numbers".

Row T(3,n) of A080853.

Equals binomial transform of [1, 3, 9, 0, 0, 0,...] - Gary W. Adamson, Apr 30 2008

a(n) is also the least weight of self-conjugate partitions having n different parts such that each part is congruent to 2 modulo 3. The first such self-conjugate partitions, corresponding to a(n)=1,2,3,4, are 2+2, 5+5+2+2+2, 8+8+5+5+5+2+2+2, 11+11+8+8+8+5+5+5+2+2+2. [Augustine O. Munagi, Dec 18 2008]

Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=3, (i>1), A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=3, a(n-1)=-coeff(charpoly(A,x),x^(n-2)). [Milan Janjic, Jan 27 2010]

REFERENCES

A. O. Munagi, Pairing conjugate partitions by residue classes, Discrete Math., 308 (2008), 2492--2501.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

G.f.: (1+x+7*x^2)/(1-x)^3.

a(n) = 9*n+a(n-1)-6 with n>0, a(0)=1. [Vincenzo Librandi, Aug 08 2010]

a(n) = n*A005448(n+1)-(n-1)*A005448(n), with A005448(0)=1. [Bruno Berselli, Jan 15 2013]

a(0)=1, a(1)=4, a(2)=16, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Jul 24 2013

MATHEMATICA

s = 1; lst = {s}; Do[s += n + 2; AppendTo[lst, s], {n, 1, 500, 9}]; lst [From Zerinvary Lajos, Jul 11 2009]

Table[(9n^2-3n+2)/2, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 4, 16}, 50] (* Harvey P. Dale, Jul 24 2013 *)

CROSSREFS

Cf. A027468, A038764. [From Augustine O. Munagi, Dec 18 2008]

Sequence in context: A054246 A173545 A080709 * A203299 A198015 A103770

Adjacent sequences:  A080852 A080853 A080854 * A080856 A080857 A080858

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Feb 23 2003

EXTENSIONS

Definition replaced with the closed form by Bruno Berselli, Jan 15 2013

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 April 19 03:44 EDT 2014. Contains 240738 sequences.