

A080855


(9*n^23*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
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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 selfconjugate partitions having n different parts such that each part is congruent to 2 modulo 3. The first such selfconjugate 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,i1]=1, and A[i,j]=0 otherwise. Then, for n>=3, a(n1)=coeff(charpoly(A,x),x^(n2)).  Milan Janjic, Jan 27 2010


REFERENCES

A. O. Munagi, Pairing conjugate partitions by residue classes, Discrete Math., 308 (2008), 24922501.


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)/(1x)^3.
a(n) = 9*n+a(n1)6 with n>0, a(0)=1.  Vincenzo Librandi, Aug 08 2010
a(n) = n*A005448(n+1)(n1)*A005448(n), with A005448(0)=1.  Bruno Berselli, Jan 15 2013
a(0)=1, a(1)=4, a(2)=16, a(n)=3*a(n1)3*a(n2)+a(n3).  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^23n+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



