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A080856 a(n) = 8*n^2 - 4*n + 1. 27
1, 5, 25, 61, 113, 181, 265, 365, 481, 613, 761, 925, 1105, 1301, 1513, 1741, 1985, 2245, 2521, 2813, 3121, 3445, 3785, 4141, 4513, 4901, 5305, 5725, 6161, 6613, 7081, 7565, 8065, 8581, 9113, 9661, 10225, 10805, 11401, 12013, 12641, 13285, 13945, 14621 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The old definition of this sequence was "Generalized polygonal numbers".
Row T(4,n) of A080853.
{a(k): 0 <= k < 3} = divisors of 25. - Reinhard Zumkeller, Jun 17 2009
Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=4, (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
Also sequence found by reading the segment (1, 5) together with the line from 5, in the direction 5, 25,..., in the square spiral whose vertices are the generalized hexagonal numbers A000217. - Omar E. Pol, Nov 05 2012
For n > 0: A049061(a(n)) = 0, when the triangle of "signed Eulerian numbers" in A049061 is seen as flattened sequence. - Reinhard Zumkeller, Jan 31 2013
LINKS
Milan Janjic, Hessenberg Matrices and Integer Sequences, J. Int. Seq. 13 (2010) # 10.7.8.
Reinhard Zumkeller, Enumerations of Divisors.
FORMULA
G.f.: (1+2*x+13*x^2)/(1-x)^3.
a(n) = A060820(n), n>0. - R. J. Mathar, Sep 18 2008
a(n) = C(n,0) + 4*C(n,1) + 16*C(n,2). - Reinhard Zumkeller, Jun 17 2009
a(n) = 16*n+a(n-1)-12 with n>0, a(0)=1. - Vincenzo Librandi, Aug 08 2010
E.g.f.: (8*x^2 + 4*x + 1)*exp(x). - G. C. Greubel, Jun 16 2017
MAPLE
A080856:=n->8*n^2 - 4*n + 1: seq(A080856(n), n=0..100); # Wesley Ivan Hurt, Jul 16 2017
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {1, 5, 25}, 80] (* Vladimir Joseph Stephan Orlovsky, Feb 17 2012 *)
PROG
(PARI) a(n)=8*n^2-4*n+1 \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
Sequence in context: A146412 A228169 A152734 * A060820 A182211 A146404
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Feb 23 2003
EXTENSIONS
Definition replaced with the closed form by Bruno Berselli, Jan 16 2013
STATUS
approved

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Last modified March 18 22:09 EDT 2024. Contains 370951 sequences. (Running on oeis4.)