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A080857
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Generalized polygonal numbers.
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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)). [From Milan R. Janjic (agnus(AT)blic.net), Jan 27 2010]
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FORMULA
| a(n)=(25n^2-15n+2)/2 G.f.: (1+3x+21x^2)/(1-x)^3
a(n)=25*n+a(n-1)-20 (with a(0)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 08 2010]
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EXAMPLE
| a(1)=25*1+1-20=6; a(2)=25*2+6-20=36; a(3)=25*3+36-20=91 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 08 2010]
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CROSSREFS
| Sequence in context: A044108 A152746 A207026 * A108158 A192278 A207106
Adjacent sequences: A080854 A080855 A080856 * A080858 A080859 A080860
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 23 2003
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