

A080857


(25*n^2  15*n + 2)/2.


1



1, 6, 36, 91, 171, 276, 406, 561, 741, 946, 1176, 1431, 1711, 2016, 2346, 2701, 3081, 3486, 3916, 4371, 4851, 5356, 5886, 6441, 7021, 7626, 8256, 8911, 9591, 10296, 11026, 11781, 12561, 13366, 14196, 15051, 15931, 16836, 17766, 18721, 19701
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


COMMENTS

The old definition of this sequence was "Generalized polygonal numbers".
Row T(5,n) of A080853.
Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=5, (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


LINKS

Table of n, a(n) for n=0..40.
M. Janjic, Hessenberg Matrices and Integer Sequences , J. Int. Seq. 13 (2010) # 10.7.8
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

G.f.: (1+3*x+21*x^2)/(1x)^3
a(n) = 25*n+a(n1)20 with n>0, a(0)=1.  Vincenzo Librandi, Aug 08 2010


MATHEMATICA

Table[(25n^215n+2)/2, {n, 0, 40}] (* or *) LinearRecurrence[{3, 3, 1}, {1, 6, 36}, 50] (* Harvey P. Dale, Aug 14 2018 *)


PROG

(PARI) a(n)=(25*n^215*n+2)/2 \\ Charles R Greathouse IV, Jun 17 2017


CROSSREFS

Sequence in context: A207171 A207454 A213189 * A108158 A207559 A207414
Adjacent sequences: A080854 A080855 A080856 * A080858 A080859 A080860


KEYWORD

nonn,easy


AUTHOR

Paul Barry, Feb 23 2003


EXTENSIONS

Definition replaced with the closed form by Bruno Berselli, Jan 16 2013


STATUS

approved



