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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A080855 (9*n^2-3*n+2)/2. 8
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 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 - 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 *)

PROG

(PARI) a(n)=binomial(3*n, 2)+1 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A027468, A038764.

Sequence in context: A173545 A080709 A256322 * 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 | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 6 09:18 EST 2016. Contains 278775 sequences.