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A080857
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(25*n^2 - 15*n + 2)/2.
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1
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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
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OFFSET
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0,2
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COMMENTS
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The old definition of this sequence was "Generalized polygonal numbers".
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
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LINKS
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FORMULA
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G.f.: (1+3*x+21*x^2)/(1-x)^3
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MATHEMATICA
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Table[(25n^2-15n+2)/2, {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 6, 36}, 50] (* Harvey P. Dale, Aug 14 2018 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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Definition replaced with the closed form by Bruno Berselli, Jan 16 2013
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STATUS
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approved
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