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 A080856 a(n) = 8*n^2 - 4*n + 1. 26
 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 G. C. Greubel, Table of n, a(n) for n = 0..5000 Milan Janjic, Hessenberg Matrices and Integer Sequences, J. Int. Seq. 13 (2010) # 10.7.8. Reinhard Zumkeller, Enumerations of Divisors. Index entries for linear recurrences with constant coefficients, signature (3,-3,1). 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 Cf. A005408, A000124, A016813, A086514, A000125, A058331, A002522, A161701, A161702, A161703, A000127, A161704, A161706, A161707, A161708, A161710, A161711, A161712, A161713, A161715, A006261. Sequence in context: A146412 A228169 A152734 * A060820 A182211 A146404 Adjacent sequences: A080853 A080854 A080855 * A080857 A080858 A080859 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 May 28 07:31 EDT 2023. Contains 362992 sequences. (Running on oeis4.)