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 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,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 LINKS 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)/(1-x)^3 a(n) = 25*n+a(n-1)-20 with n>0, a(0)=1. - Vincenzo Librandi, Aug 08 2010 MATHEMATICA Table[(25n^2-15n+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^2-15*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

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Last modified January 18 16:27 EST 2020. Contains 331011 sequences. (Running on oeis4.)