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A083067
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6th row of number array A083064.
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5
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1, 6, 41, 286, 2001, 14006, 98041, 686286, 4804001, 33628006, 235396041, 1647772286, 11534406001, 80740842006, 565185894041, 3956301258286, 27694108808001, 193858761656006, 1357011331592041, 9499079321144286
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform of A052934 - Paul Barry (pbarry(AT)wit.ie), Apr 30 2003
Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=9, (i>1), A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n-1)=(-1)^(n-1)*charpoly(A,2). [From Milan R. Janjic (agnus(AT)blic.net), Feb 21 2010]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index to sequences with linear recurrences with constant coefficients, signature (8,-7).
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FORMULA
| a(n) = (5*7^n+1)/6.
G.f.: (1-2*x)/((1-7*x)*(1-x)).
E.g.f.: (5*exp(7*x)+exp(x))/6.
a(n) = 7*a(n-1)-1 (with a(0)=1). - Vincenzo Librandi, Aug 08 2010
a(n) = 8*a(n-1)-7*a(n-2. - Vincenzo Librandi, Nov 06 2011
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MATHEMATICA
| f[n_]:=7^n; lst={}; Do[a=f[n]; Do[a-=f[m], {m, n-1, 1, -1}]; AppendTo[lst, a/7], {n, 1, 30}]; lst [From Vladimir Orlovsky, Feb 10 2010]
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PROG
| (MAGMA) [(5*7^n+1)/6: n in [0..30]]; // Vincenzo Librandi, Nov 06 2011
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CROSSREFS
| Cf. A083066, A083068.
Sequence in context: A049685 A196954 A122371 * A000402 A186654 A152107
Adjacent sequences: A083064 A083065 A083066 * A083068 A083069 A083070
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KEYWORD
| nonn,easy
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Apr 21 2003
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