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A083066
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5th row of number array A083064.
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8
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1, 5, 29, 173, 1037, 6221, 37325, 223949, 1343693, 8062157, 48372941, 290237645, 1741425869, 10448555213, 62691331277, 376147987661, 2256887925965, 13541327555789, 81247965334733, 487487792008397, 2924926752050381
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=8, (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 (7,-6).
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FORMULA
| a(n) = (4*6^n+1)/5.
G.f.: (1-2*x)/((1-6*x)*(1-x)).
E.g.f.: (4*exp(6*x)+exp(x))/5.
a(n) = 6*a(n-1)-1 (with a(0)=1). - Vincenzo Librandi, Aug 08 2010
a(n) = 7*a(n-1)-6*a(n-2). - Vincenzo Librandi, Nov 04 2011
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MATHEMATICA
| f[n_]:=6^n; lst={}; Do[a=f[n]; Do[a-=f[m], {m, n-1, 1, -1}]; AppendTo[lst, a/6], {n, 1, 30}]; lst [From Vladimir Orlovsky, Feb 10 2010]
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PROG
| (MAGMA) [(4*6^n+1)/5: n in [0..30]]; // Vincenzo Librandi, Nov 06 2011
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CROSSREFS
| Cf. A083065, A083067.
Sequence in context: A122370 A088349 A137625 * A163611 A160906 A163073
Adjacent sequences: A083063 A083064 A083065 * A083067 A083068 A083069
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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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